<doc:document xmlns:doc="http://www.elsevier.com/xml/document/schema" xmlns:dp="http://www.elsevier.com/xml/common/doc-properties/schema" xmlns:cps="http://www.elsevier.com/xml/common/consyn-properties/schema" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dct="http://purl.org/dc/terms/" xmlns:prism="http://prismstandard.org/namespaces/basic/2.0/" xmlns:oa="http://vtw.elsevier.com/data/ns/properties/OpenAccess-1/" xmlns:cp="http://vtw.elsevier.com/data/ns/properties/Copyright-1/" xmlns:cja="http://www.elsevier.com/xml/cja/schema" xmlns:ja="http://www.elsevier.com/xml/ja/schema" xmlns:bk="http://www.elsevier.com/xml/bk/schema" xmlns:ce="http://www.elsevier.com/xml/common/schema" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:cals="http://www.elsevier.com/xml/common/cals/schema" xmlns:tb="http://www.elsevier.com/xml/common/table/schema" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/schema" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/schema" xmlns:xlink="http://www.w3.org/1999/xlink"><rdf:RDF><rdf:Description rdf:about="http://dx.doi.org/10.1016/j.physletb.2007.04.006"><dct:format>application/xml</dct:format><dct:title>Mass measurements of neutron-rich nuclei near the [formula omitted] and 28 shell closures</dct:title><dct:creator>B. Jurado</dct:creator><dct:creator>H. Savajols</dct:creator><dct:creator>W. Mittig</dct:creator><dct:creator>N.A. Orr</dct:creator><dct:creator>P. Roussel-Chomaz</dct:creator><dct:creator>D. Baiborodin</dct:creator><dct:creator>W.N. Catford</dct:creator><dct:creator>M. Chartier</dct:creator><dct:creator>C.E. Demonchy</dct:creator><dct:creator>Z. Dlouhý</dct:creator><dct:creator>A. Gillibert</dct:creator><dct:creator>L. Giot</dct:creator><dct:creator>A. Khouaja</dct:creator><dct:creator>A. Lépine-Szily</dct:creator><dct:creator>S. Lukyanov</dct:creator><dct:creator>J. Mrazek</dct:creator><dct:creator>Y.E. Penionzhkevich</dct:creator><dct:creator>S. Pita</dct:creator><dct:creator>M. Rousseau</dct:creator><dct:creator>A.C. Villari</dct:creator><dct:description>Physics Letters B 649 (2007) 43-48. doi:10.1016/j.physletb.2007.04.006</dct:description><prism:aggregationType>journal</prism:aggregationType><prism:publicationName>Physics Letters B</prism:publicationName><prism:copyright>Copyright © 2007 Elsevier B.V. All rights reserved.</prism:copyright><dct:publisher>Elsevier B.V.</dct:publisher><prism:issn>0370-2693</prism:issn><prism:volume>649</prism:volume><prism:number>1</prism:number><prism:coverDisplayDate>24 May 2007</prism:coverDisplayDate><prism:coverDate>2007-05-24</prism:coverDate><prism:pageRange>43-48</prism:pageRange><prism:startingPage>43</prism:startingPage><prism:endingPage>48</prism:endingPage><prism:doi>10.1016/j.physletb.2007.04.006</prism:doi><prism:url>http://dx.doi.org/10.1016/j.physletb.2007.04.006</prism:url><dct:identifier>doi:10.1016/j.physletb.2007.04.006</dct:identifier><oa:openAccessInformation><oa:openAccessStatus xmlns:cp="http://www.elsevier.com/xml/common/consyn-properties/schema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full</oa:openAccessStatus><oa:openAccessEffective xmlns:cp="http://www.elsevier.com/xml/common/consyn-properties/schema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">2014-01-01T00:14:32Z</oa:openAccessEffective><oa:sponsor xmlns:cp="http://www.elsevier.com/xml/common/consyn-properties/schema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><oa:sponsorName>SCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physics</oa:sponsorName><oa:sponsorType>http://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBody</oa:sponsorType></oa:sponsor><oa:userLicense xmlns:cp="http://www.elsevier.com/xml/common/consyn-properties/schema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">http://creativecommons.org/licenses/by/3.0/</oa:userLicense></oa:openAccessInformation></rdf:Description></rdf:RDF><dp:document-properties><dp:aggregation-type>Journals</dp:aggregation-type><dp:version-number>S300.2</dp:version-number></dp:document-properties><ja:article docsubtype="sco" xml:lang="en" version="5.0"><ja:item-info><ja:jid>PLB</ja:jid><ja:aid>23903</ja:aid><ce:pii>S0370-2693(07)00433-9</ce:pii><ce:doi>10.1016/j.physletb.2007.04.006</ce:doi><ce:copyright type="full-transfer" year="2007">Elsevier B.V.</ce:copyright><ce:doctopics><ce:doctopic><ce:text>Experiments</ce:text></ce:doctopic></ce:doctopics></ja:item-info><ce:floats><ce:figure id="fig001"><ce:label>Fig. 1</ce:label><ce:caption><ce:simple-para view="all"><mml:math altimg="si27.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> as a function of <mml:math altimg="si28.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> where <ce:italic>N</ce:italic> is the neutron number. The triangles are from the mass table <ce:cross-ref refid="bib012">[12]</ce:cross-ref>, the diamonds and the squares represent the new and improved (respectively) results measured in the present work.</ce:simple-para></ce:caption><ce:link locator="fgr001"/></ce:figure><ce:figure id="fig002"><ce:label>Fig. 2</ce:label><ce:caption><ce:simple-para view="all">Experimental results for the three-point indicator <mml:math altimg="si50.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> as function of neutron number. The same symbols are used as in <ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref>. The dashed lines link the values of <mml:math altimg="si51.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> for even-<ce:italic>N</ce:italic> nuclei and the full lines for odd-<ce:italic>N</ce:italic> nuclei. The vertical lines indicate the position of <ce:italic>N</ce:italic>=20 and 28.</ce:simple-para></ce:caption><ce:link locator="fgr002"/></ce:figure><ce:figure id="fig003"><ce:label>Fig. 3</ce:label><ce:caption><ce:simple-para view="all">The microscopic correction as function of neutron number. The same symbols are used as in <ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref>. The vertical lines indicate the position of <ce:italic>N</ce:italic>=20 and 28.</ce:simple-para></ce:caption><ce:link locator="fgr003"/></ce:figure><ce:figure id="fig004"><ce:label>Fig. 4</ce:label><ce:caption><ce:simple-para view="all">Experimental values of <mml:math altimg="si97.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> for the <ce:italic>Z</ce:italic>=14 isotopic chain in comparison with three different mass formulas (see text). The vertical lines indicate the position of <ce:italic>N</ce:italic>=20 and 28.</ce:simple-para></ce:caption><ce:link locator="fgr004"/></ce:figure><ce:table id="tbl001" frame="topbot" rowsep="0" colsep="0"><ce:label>Table 1</ce:label><ce:caption><ce:simple-para view="all">Experimental atomic mass excesses (±uncertainties) in keV. In the last column the weighted mean of columns 2 and 3 is given</ce:simple-para></ce:caption><cals:tgroup cols="4"><cals:colspec colnum="1" colname="col1" align="left"/><cals:colspec colnum="2" colname="col2" align="left"/><cals:colspec colnum="3" colname="col3" align="left"/><cals:colspec colnum="4" colname="col4" align="left"/><cals:thead valign="top"><cals:row rowsep="1"><ce:entry/><ce:entry>This work</ce:entry><ce:entry>Ref. <ce:cross-ref refid="bib012">[12]</ce:cross-ref></ce:entry><ce:entry>Mean</ce:entry></cals:row></cals:thead><cals:tbody valign="top"><cals:row><ce:entry><ce:sup loc="pre">23</ce:sup>N</ce:entry><ce:entry>36680(860)</ce:entry><ce:entry/><ce:entry>36680(860)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">23</ce:sup>O</ce:entry><ce:entry>14620(100)</ce:entry><ce:entry>14610(120)</ce:entry><ce:entry>14620(80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">24</ce:sup>O</ce:entry><ce:entry>18500(110)</ce:entry><ce:entry>19070(240)</ce:entry><ce:entry>18600(100)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">25</ce:sup>F</ce:entry><ce:entry>11410( 90)</ce:entry><ce:entry>11270(100)</ce:entry><ce:entry>11350( 70)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">26</ce:sup>F</ce:entry><ce:entry>18680( 80)</ce:entry><ce:entry>18270(170)</ce:entry><ce:entry>18610( 70)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">27</ce:sup>F</ce:entry><ce:entry>24630(190)</ce:entry><ce:entry>24930(380)</ce:entry><ce:entry>24690(170)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">27</ce:sup>Ne</ce:entry><ce:entry>7020( 70)</ce:entry><ce:entry>7070(110)</ce:entry><ce:entry>7030( 60)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">28</ce:sup>Ne</ce:entry><ce:entry>11280(110)</ce:entry><ce:entry>11240(150)</ce:entry><ce:entry>11270( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">29</ce:sup>Ne</ce:entry><ce:entry>18400(100)</ce:entry><ce:entry>18060(270)</ce:entry><ce:entry>18360( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">30</ce:sup>Ne</ce:entry><ce:entry>23040(280)</ce:entry><ce:entry>23100(570)</ce:entry><ce:entry>23050(250)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">31</ce:sup>Ne</ce:entry><ce:entry>30820(1620)</ce:entry><ce:entry/><ce:entry>30820(1620)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">31</ce:sup>Na</ce:entry><ce:entry>12520(110)</ce:entry><ce:entry>12650(210)</ce:entry><ce:entry>12550(100)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">32</ce:sup>Na</ce:entry><ce:entry>18810(120)</ce:entry><ce:entry>19060(360)</ce:entry><ce:entry>18840(110)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">33</ce:sup>Na</ce:entry><ce:entry>23420(350)</ce:entry><ce:entry>24890(870)</ce:entry><ce:entry>23630(330)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">34</ce:sup>Mg</ce:entry><ce:entry>8560( 90)</ce:entry><ce:entry>8810(230)</ce:entry><ce:entry>8590( 80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">35</ce:sup>Mg</ce:entry><ce:entry>15640(180)</ce:entry><ce:entry/><ce:entry>15640(180)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">36</ce:sup>Mg</ce:entry><ce:entry>20380(460)</ce:entry><ce:entry/><ce:entry>20380(460)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">34</ce:sup>Al</ce:entry><ce:entry>−3100( 80)</ce:entry><ce:entry>−2930(110)</ce:entry><ce:entry>−3040( 70)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">35</ce:sup>Al</ce:entry><ce:entry>−220( 70)</ce:entry><ce:entry>−130(180)</ce:entry><ce:entry>−210( 70)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">36</ce:sup>Al</ce:entry><ce:entry>5950(100)</ce:entry><ce:entry>5780(210)</ce:entry><ce:entry>5920( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">37</ce:sup>Al</ce:entry><ce:entry>9810(120)</ce:entry><ce:entry>9950(330)</ce:entry><ce:entry>9830(110)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">38</ce:sup>Al</ce:entry><ce:entry>16210(250)</ce:entry><ce:entry>16050(730)</ce:entry><ce:entry>16190(240)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">39</ce:sup>Al</ce:entry><ce:entry>20170(630)</ce:entry><ce:entry>21400(1470)</ce:entry><ce:entry>20360(580)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">36</ce:sup>Si</ce:entry><ce:entry>−12370(110)</ce:entry><ce:entry>−12480(120)</ce:entry><ce:entry>−12420( 80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">37</ce:sup>Si</ce:entry><ce:entry>−6620( 90)</ce:entry><ce:entry>−6580(170)</ce:entry><ce:entry>−6610( 80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">38</ce:sup>Si</ce:entry><ce:entry>−4170( 70)</ce:entry><ce:entry>−4070(140)</ce:entry><ce:entry>−4150( 60)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">39</ce:sup>Si</ce:entry><ce:entry>2320( 90)</ce:entry><ce:entry>1930(340)</ce:entry><ce:entry>2290( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">40</ce:sup>Si</ce:entry><ce:entry>5430(230)</ce:entry><ce:entry>5470(560)</ce:entry><ce:entry>5440(210)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">41</ce:sup>Si</ce:entry><ce:entry>12120(370)</ce:entry><ce:entry>13560(1840)</ce:entry><ce:entry>12170(360)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">42</ce:sup>Si</ce:entry><ce:entry>15160(580)</ce:entry><ce:entry/><ce:entry>15160(580)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">40</ce:sup>P</ce:entry><ce:entry>−8030(120)</ce:entry><ce:entry>−8110(140)</ce:entry><ce:entry>−8060( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">41</ce:sup>P</ce:entry><ce:entry>−4980( 80)</ce:entry><ce:entry>−5280(220)</ce:entry><ce:entry>−5020( 80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">42</ce:sup>P</ce:entry><ce:entry>1010(210)</ce:entry><ce:entry>940(450)</ce:entry><ce:entry>1000(190)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">43</ce:sup>P</ce:entry><ce:entry>4680(370)</ce:entry><ce:entry>5770(970)</ce:entry><ce:entry>4820(346)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">44</ce:sup>P</ce:entry><ce:entry>9380(900)</ce:entry><ce:entry/><ce:entry>9380(900)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">40</ce:sup>S</ce:entry><ce:entry>−22940(120)</ce:entry><ce:entry>−22870(140)</ce:entry><ce:entry>−22910( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">43</ce:sup>S</ce:entry><ce:entry>−12070(100)</ce:entry><ce:entry>−11970(200)</ce:entry><ce:entry>−12050( 90)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">44</ce:sup>S</ce:entry><ce:entry>−9100(140)</ce:entry><ce:entry>−9120(390)</ce:entry><ce:entry>−9100(130)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">45</ce:sup>S</ce:entry><ce:entry>−3990(690)</ce:entry><ce:entry>−3250(1740)</ce:entry><ce:entry>−3890(640)</ce:entry></cals:row><cals:row><ce:entry><ce:vsp sp="0.4"/></ce:entry><ce:entry/><ce:entry/><ce:entry/></cals:row><cals:row><ce:entry><ce:sup loc="pre">43</ce:sup>Cl</ce:entry><ce:entry>−24120(130)</ce:entry><ce:entry>−24170(160)</ce:entry><ce:entry>−24140(100)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">45</ce:sup>Cl</ce:entry><ce:entry>−18360(100)</ce:entry><ce:entry>−18360(120)</ce:entry><ce:entry>−18360( 80)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">46</ce:sup>Cl</ce:entry><ce:entry>−13810(160)</ce:entry><ce:entry>−14710(720)</ce:entry><ce:entry>−13850(160)</ce:entry></cals:row><cals:row><ce:entry><ce:sup loc="pre">47</ce:sup>Cl</ce:entry><ce:entry>−8920(1000)</ce:entry><ce:entry/><ce:entry>−8920(1000)</ce:entry></cals:row></cals:tbody></cals:tgroup></ce:table></ce:floats><ja:head><ce:title>Mass measurements of neutron-rich nuclei near the <mml:math altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28 shell closures</ce:title><ce:author-group><ce:author><ce:given-name>B.</ce:given-name><ce:surname>Jurado</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref><ce:cross-ref refid="cor001"><ce:sup loc="post">⁎</ce:sup></ce:cross-ref><ce:e-address type="email">jurado@cenbg.in2p3.fr</ce:e-address></ce:author><ce:author><ce:given-name>H.</ce:given-name><ce:surname>Savajols</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>W.</ce:given-name><ce:surname>Mittig</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>N.A.</ce:given-name><ce:surname>Orr</ce:surname><ce:cross-ref refid="aff002"><ce:sup loc="post">b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>P.</ce:given-name><ce:surname>Roussel-Chomaz</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>D.</ce:given-name><ce:surname>Baiborodin</ce:surname><ce:cross-ref refid="aff003"><ce:sup loc="post">c</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>W.N.</ce:given-name><ce:surname>Catford</ce:surname><ce:cross-ref refid="aff004"><ce:sup loc="post">d</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>M.</ce:given-name><ce:surname>Chartier</ce:surname><ce:cross-ref refid="aff005"><ce:sup loc="post">e</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>C.E.</ce:given-name><ce:surname>Demonchy</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Z.</ce:given-name><ce:surname>Dlouhý</ce:surname><ce:cross-ref refid="aff003"><ce:sup loc="post">c</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.</ce:given-name><ce:surname>Gillibert</ce:surname><ce:cross-ref refid="aff006"><ce:sup loc="post">f</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>L.</ce:given-name><ce:surname>Giot</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.</ce:given-name><ce:surname>Khouaja</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.</ce:given-name><ce:surname>Lépine-Szily</ce:surname><ce:cross-ref refid="aff007"><ce:sup loc="post">g</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>S.</ce:given-name><ce:surname>Lukyanov</ce:surname><ce:cross-ref refid="aff008"><ce:sup loc="post">h</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>J.</ce:given-name><ce:surname>Mrazek</ce:surname><ce:cross-ref refid="aff003"><ce:sup loc="post">c</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Y.E.</ce:given-name><ce:surname>Penionzhkevich</ce:surname><ce:cross-ref refid="aff008"><ce:sup loc="post">h</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>S.</ce:given-name><ce:surname>Pita</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>M.</ce:given-name><ce:surname>Rousseau</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.C.</ce:given-name><ce:surname>Villari</ce:surname><ce:cross-ref refid="aff001"><ce:sup loc="post">a</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="aff001"><ce:label>a</ce:label><ce:textfn>GANIL, BP 5027, 14076 Caen cedex 05, France</ce:textfn></ce:affiliation><ce:affiliation id="aff002"><ce:label>b</ce:label><ce:textfn>LPC-Caen, ENSICAEN, IN2P3-CNRS et Université de Caen,14050 Caen cedex, France</ce:textfn></ce:affiliation><ce:affiliation id="aff003"><ce:label>c</ce:label><ce:textfn>NPI, ASCR, 250 68 Řež, Czech Republic</ce:textfn></ce:affiliation><ce:affiliation id="aff004"><ce:label>d</ce:label><ce:textfn>Department of Physics, University of Surrey, Guilford, GU27XH, UK</ce:textfn></ce:affiliation><ce:affiliation id="aff005"><ce:label>e</ce:label><ce:textfn>Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK</ce:textfn></ce:affiliation><ce:affiliation id="aff006"><ce:label>f</ce:label><ce:textfn>CEA/DSM/DAPNIA/SPhN, 91191Gif-sur-Yvette, France</ce:textfn></ce:affiliation><ce:affiliation id="aff007"><ce:label>g</ce:label><ce:textfn>IFUSP-Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo, Brazil</ce:textfn></ce:affiliation><ce:affiliation id="aff008"><ce:label>h</ce:label><ce:textfn>FLNR, JINR, Dubna, P.O. Box 79, 101 000 Moscow, Russia</ce:textfn></ce:affiliation><ce:correspondence id="cor001"><ce:label>⁎</ce:label><ce:text>Corresponding author. Present address: CENBG, F-33175 Gradignan, France.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="20" month="12" year="2006"/><ce:date-revised day="16" month="2" year="2007"/><ce:date-accepted day="3" month="4" year="2007"/><ce:miscellaneous>Editor: V. Metag</ce:miscellaneous><ce:abstract class="author"><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para view="all">Mass measurements of very neutron-rich nuclei near the <mml:math altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28 shell closures are presented. Seven masses have been determined for the first time and the precision of 36 masses has been significantly improved. These results are used to investigate the evolution of the odd–even staggering of binding energies with neutron number. Special attention is paid to the evolution of the <mml:math altimg="si3.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> shell closure as the neutron dripline is approached. Changes in shell structure are observed around <mml:math altimg="si4.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> for the P and S isotopes but not for Si. This may be interpreted as a persistence of the shell closure at <mml:math altimg="si5.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> or as the result of a very sudden onset in deformation at <ce:sup loc="pre">42</ce:sup>Si.</ce:simple-para></ce:abstract-sec></ce:abstract></ja:head><ja:body view="all"><ce:sections><ce:para view="all">The mass of a quantum mechanical system, such as the nucleus, is a fundamental quantity as it reflects the sum of all forces acting on it. Of particular interest are direct mass measurements far from the valley of stability (such as those described in this work) which permit tests of the reliability of nuclear mass models to be made and studies of the evolution of shell or subshell closures and correlations to be undertaken. However, the direct measurement of masses far from stability presents significant technical challenges. The principal one being the limited production cross sections. In addition, exotic nuclides are by definition very short lived. The development of a fast measurement technique is therefore imperative, but such technique must also be of sufficiently high resolution to make precision measurements. In the present work we describe how the time-of-flight technique using the SPEG spectrometer <ce:cross-ref refid="bib001">[1]</ce:cross-ref> at GANIL has been improved in order to determine the masses of very neutron-rich nuclei in the vicinity of <mml:math altimg="si6.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28. The results are then used to study the evolution of the odd–even staggering (OES) of nuclear masses with neutron number. When representing nuclear masses as a function of the neutron number one observes that even-neutron-number nuclei are more strongly bound than their odd-neutron-number neighbors. The OES originates from two fundamental physical mechanisms: the breaking of the mean-field spherical symmetry and pairing correlations <ce:cross-ref refid="bib002">[2]</ce:cross-ref>. Both mechanisms are strongly influenced by the number of neutrons. For instance, it is now well established that deformation effects are responsible for the vanishing of the <mml:math altimg="si7.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> shell closure for the very neutron-rich sodium and magnesium isotopes (see, for example, Refs. <ce:cross-refs refid="bib003 bib004 bib005">[3–5]</ce:cross-refs>). Particle correlations occur mostly in a narrow zone of the phase space around the Fermi surface. In drip-line nuclei the Fermi surface is very close to the single-particle continuum. Consequently, the scattering of virtual pairs into the continuum has to be considered. The increase in neutron-pairing correlations as the neutron binding energy decreases seems to be a quite general result of calculations that include continuum effects (see for example Refs. <ce:cross-refs refid="bib006 bib007 bib008 bib009">[6–9]</ce:cross-refs>). Our results also provide key information to investigate the evolution of the <mml:math altimg="si8.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> shell closure when approaching the neutron dripline. Deformation effects and the vanishing of the spin–orbit force could cause an erosion of this shell closure for very neutron-rich nuclei. Finally, our results will be used to check the predictive power of several mass formulas.</ce:para><ce:para view="all">For direct mass measurements of exotic nuclei three main issues have to be faced: the production rates, the mass resolution and the systematic errors. A series of earlier mass measurements <ce:cross-ref refid="bib010">[10]</ce:cross-ref> (and references therein) has shown that this can be achieved at GANIL by combining a time-of-flight (TOF) technique with the high-resolution energy-loss spectrometer SPEG. The very broad elemental and isotopic distributions resulting from heavy-ion projectile fragmentation reactions combined with fast in-flight magnetic selection allows the mapping of an entire region of the nuclear mass surface in a single measurement. Compared to other mass measurement methods, the availability at GANIL of very intense neutron-rich beams (such as <ce:sup loc="pre">48</ce:sup>Ca) together with the relatively high transmission rates through the SISSI device <ce:cross-ref refid="bib011">[11]</ce:cross-ref> and the alpha-spectrometer<ce:cross-ref refid="fn001"><ce:sup loc="post">1</ce:sup></ce:cross-ref><ce:footnote id="fn001"><ce:label>1</ce:label><ce:note-para>A feature arising from the strong forward focusing of the fragmentation products.</ce:note-para></ce:footnote> enables measurements to be made far from stability with reasonable yields. Nuclei with lifetimes as short as the flight time through the system of <mml:math altimg="si9.gif" display="inline" overflow="scroll"><mml:mo>∼</mml:mo><mml:mn>1</mml:mn><mml:mtext> </mml:mtext><mml:mtext>μs</mml:mtext></mml:math> can be measured. The nuclei investigated here were produced by fragmentation of a <ce:sup loc="pre">48</ce:sup>Ca beam of 4 μAe at 60.3⋅A MeV on a Ta target. The TOF technique requires the simultaneous determination of the masses of well-known nuclei for calibration. Consequently, apart from the neutron-rich nuclei of interest, it is of great importance to measure simultaneously a broad range of reference nuclei. To achieve this, a Ta production target with three different thicknesses and two magnetic rigidities of the beam line and spectrometer were employed. In addition, a thin (25 μm) Be achromatic degrader was placed at the dispersive focal plane of the alpha spectrometer. In this manner, the light ions that caused saturation and pile-up in the detection system in previous measurements were eliminated. As a consequence, the <ce:sup loc="pre">48</ce:sup>Ca beam intensity could be increased by more than one order of magnitude with respect to the previous experiment <ce:cross-ref refid="bib010">[10]</ce:cross-ref>.</ce:para><ce:para view="all">The principle of mass determination by means of the TOF technique relies on the relation between the magnetic rigidity, <ce:italic>Bρ</ce:italic>, and the velocity, <ce:italic>v</ce:italic>, of an ion of rest mass, <mml:math altimg="si10.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>m</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>, and charge, <ce:italic>q</ce:italic>, traversing an achromatic system: <mml:math altimg="si11.gif" display="inline" overflow="scroll"><mml:mi>B</mml:mi><mml:mi>ρ</mml:mi><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:msub><mml:mi>m</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mi>v</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>q</mml:mi></mml:math>, where <ce:italic>γ</ce:italic> is the Lorentz factor. A precise measurement of the magnetic rigidity and the velocity allows the ratio <mml:math altimg="si12.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">exp</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mi>q</mml:mi></mml:math> (where <mml:math altimg="si13.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">exp</mml:mi></mml:mrow></mml:msub></mml:math> is the experimental value of the mass of the ion) to be deduced. Once the ion has been identified in <ce:italic>A</ce:italic>, <ce:italic>q</ce:italic> and <ce:italic>Z</ce:italic>, <mml:math altimg="si14.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">exp</mml:mi></mml:mrow></mml:msub></mml:math> can be extracted. The velocity of the ions is obtained from the TOF measurement. Detailed descriptions of the technique may be found in <ce:cross-ref refid="bib010">[10]</ce:cross-ref> and references therein.</ce:para><ce:para view="all">The atomic mass excesses are obtained by means of a multidimensional fit where the mass excess is expressed as a Taylor series development of the form (for <mml:math altimg="si15.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi></mml:math>),<ce:display><ce:formula><mml:math altimg="si16.gif" display="inline" overflow="scroll"><mml:msup><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">exp</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mi>Z</mml:mi><mml:mo>+</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mfrac><mml:mi>A</mml:mi><mml:mi>Z</mml:mi></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mn>3</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mn>4</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mi>Z</mml:mi><mml:mo>+</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mi>Z</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mfrac><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>,</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>E</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:math></ce:formula></ce:display></ce:para><ce:para view="all">The constant <mml:math altimg="si17.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mi>α</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup></mml:math> and the first order terms serve to transform <mml:math altimg="si18.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">exp</mml:mi></mml:mrow></mml:msub></mml:math> into the atomic mass excess. The function <mml:math altimg="si19.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mi>f</mml:mi><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:msubsup></mml:math>, which is a linear combination of higher-order terms in <mml:math altimg="si20.gif" display="inline" overflow="scroll"><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>,</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>Z</mml:mi></mml:math> and <ce:italic>AZ</ce:italic>, and the energy-loss (Δ<ce:italic>E</ce:italic>) dependent function <mml:math altimg="si21.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mi>f</mml:mi><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:msubsup></mml:math> are required to correct for the systematic uncertainties associated with the technique. In contrast to previous experiments where no achromatic degrader was employed, higher order terms were required here to correct for the associated aberrations. The coefficients of the fit <mml:math altimg="si22.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:msubsup></mml:math> are obtained by minimizing the difference between the experimental and the adopted reference mass excesses of the 2003 atomic-mass evaluation <ce:cross-ref refid="bib012">[12]</ce:cross-ref>. The unknown masses are then determined using the coefficients and functions from the best fit. The uncertainties associated with such a determination arise not only from the statistical uncertainty, but also from the need inherent in the method to interpolate between and extrapole from the reference masses, as well as the systematic uncertainties which are a measure of the limiting precision of the measurement. In the present work a number of <ce:italic>independent</ce:italic> measurements<ce:cross-ref refid="fn002"><ce:sup loc="post">2</ce:sup></ce:cross-ref><ce:footnote id="fn002"><ce:label>2</ce:label><ce:note-para>These corresponded to runs with different settings of the rigidity of beamline and spectrometer, together with a parallel chain of electronics.</ce:note-para></ce:footnote> were made resulting in up to 5 independent mass determinations (denoted by the index “<ce:italic>j</ce:italic>”) for many of the nuclei. Each measurement was analyzed separately following the procedure outlined above. The uncertainty <mml:math altimg="si23.gif" display="inline" overflow="scroll"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msup><mml:mi>M</mml:mi><mml:mi>j</mml:mi></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> for each measurement was determined from the combination in quadrature of the statistical and the systematic errors. The statistical error varied from a few tens of keV for nuclei situated close to the line of stability, to around 1 MeV for nuclei in the vicinity of the neutron dripline where the production rates were very low. The systematic error for each of the measurements was estimated to be 150 keV. The final mass excesses, <mml:math altimg="si24.gif" display="inline" overflow="scroll"><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, quoted in <ce:cross-ref refid="tbl001">Table 1</ce:cross-ref><ce:float-anchor refid="tbl001"/>, are the weighted means of the masses derived from each of the independent measurements. In the present experiment several combinations of higher order terms allowed acceptable fits (as defined by the chi-squared per degree of freedom) to be obtained. The variations in the masses derived from these fits provided a measure<ce:cross-ref refid="fn003"><ce:sup loc="post">3</ce:sup></ce:cross-ref><ce:footnote id="fn003"><ce:label>3</ce:label><ce:note-para>Estimated by calculating the dispersion between the results of the acceptable fits <mml:math altimg="si25.gif" display="inline" overflow="scroll"><mml:msup><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> and the final adopted mass excesses—<mml:math altimg="si26.gif" display="inline" overflow="scroll"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">ext</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:msup><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:math>.</ce:note-para></ce:footnote> of the uncertainty arising from the extrapolations noted above. The uncertainty in the adopted mass excesses (<ce:cross-ref refid="tbl001">Table 1</ce:cross-ref>) was thus derived as the combination in quadrature of that of the weighted mean and that determined for the extrapolation. The results of the analysis described above are listed in <ce:cross-ref refid="tbl001">Table 1</ce:cross-ref>, where seven new masses can be seen to have been determined: <ce:sup loc="pre">23</ce:sup>N, <ce:sup loc="pre">31</ce:sup>Ne, <ce:sup loc="pre">35</ce:sup>Mg, <ce:sup loc="pre">36</ce:sup>Mg, <ce:sup loc="pre">42</ce:sup>Si, <ce:sup loc="pre">44</ce:sup>P and <ce:sup loc="pre">47</ce:sup>Cl. In addition, the precision of 36 masses has been considerably improved with respect to the compilation of Ref. <ce:cross-ref refid="bib012">[12]</ce:cross-ref>. No statistically significant discrepancies between our results and the 2003 atomic-mass evaluation <ce:cross-ref refid="bib012">[12]</ce:cross-ref> are observed to occur.</ce:para><ce:para view="all">The one-neutron separation energy <mml:math altimg="si29.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> is the most straightforward observable reflecting the OES of binding energies. It is defined as:<ce:display><ce:formula><mml:math altimg="si30.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math></ce:formula></ce:display> where <mml:math altimg="si31.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>M</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> is the neutron mass excess. In order to illustrate the odd–even staggering, <ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref><ce:float-anchor refid="fig001"/> plots <mml:math altimg="si32.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> as a function of <mml:math altimg="si33.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> for four isotopic chains. Two diagonal lines can be clearly distinguished. The upper line corresponds to nuclei with an even neutron number <mml:math altimg="si34.gif" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> for the ordinate which are more strongly bound. The lower line corresponds to nuclei with an even neutron number <mml:math altimg="si35.gif" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> on the abscissa. The separation between the two lines reflects the intensity of the odd–even staggering. Indeed, it is easy to see that if <mml:math altimg="si36.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mtext>const</mml:mtext><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:math> for even <ce:italic>N</ce:italic>, and <mml:math altimg="si37.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mtext>const</mml:mtext></mml:math> for odd <ce:italic>N</ce:italic>, the points formed in a diagram <mml:math altimg="si38.gif" display="inline" overflow="scroll"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math altimg="si39.gif" display="inline" overflow="scroll"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> will lie on two lines, <mml:math altimg="si40.gif" display="inline" overflow="scroll"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:math> and <mml:math altimg="si41.gif" display="inline" overflow="scroll"><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:math>. The separation between these two lines is then equal to <mml:math altimg="si42.gif" display="inline" overflow="scroll"><mml:mi>δ</mml:mi><mml:mo>⋅</mml:mo><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:math>. The nuclei with the lowest <mml:math altimg="si43.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> are the most neutron-rich ones. This original diagram is therefore well suited to trace the dependence of the OES on binding energy. The OES staggering is often taken as an indicator of the strength of pairing correlations. As outlined above, most of the theories including continuum effects predict an increase in neutron pairing correlations with increasing <mml:math altimg="si44.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>Z</mml:mi></mml:math>. However, our results indicate that this does not translate to an increase in the OES. Instead, <ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref> shows an overall reduction of the OES when the binding energy decreases for <mml:math altimg="si45.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:math> and 12. A strong attenuation of the OES close to the neutron dripline has been predicted for fluorine isotopes by <ce:cross-ref refid="bib007">[7]</ce:cross-ref>. As described in Ref. <ce:cross-ref refid="bib007">[7]</ce:cross-ref>, this does not imply a decrease in the pairing correlations as a decrease in the OES may result from the np-continuum coupling, even if pairing increases. Here, as noted above, we see such a reduction not only for <mml:math altimg="si46.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:math>, 12 (<ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref>) but also for the oxygen isotopes (not shown). For all the other elements the OES attenuation is less evident and we observe a stabilization in the OES when approaching the neutron dripline. To illustrate this the <mml:math altimg="si47.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>13</mml:mn></mml:math> and 14 isotopic chains are also shown in <ce:cross-ref refid="fig001">Fig. 1</ce:cross-ref>, whereby the OES staggering gap is clearly apparent but for the lowest values of <mml:math altimg="si48.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> the separation between the two groups of data remains rather constant. This indicates that features other than correlations are important. For instance, the spin–isospin coupling, discussed in Ref. <ce:cross-ref refid="bib013">[13]</ce:cross-ref>, and thought to be responsible for the deformation effects around <mml:math altimg="si49.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math>, will introduce an effect dependent on the filling of shells.</ce:para><ce:para view="all">Several theoretical studies have investigated how to separate the pairing and the mean-field contributions to the OES. The authors of Refs. <ce:cross-refs refid="bib002 bib014">[2,14]</ce:cross-refs> proposed to extract the pairing contribution to the OES from experimental data by using the three-point indicator:<ce:display><ce:formula><mml:math altimg="si52.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>]</mml:mo></mml:mrow><mml:msup><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn><mml:mo>.</mml:mo></mml:math></ce:formula></ce:display> It was demonstrated in Ref. <ce:cross-ref refid="bib002">[2]</ce:cross-ref>, that the indicator <mml:math altimg="si53.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> evaluated for odd-<ce:italic>N</ce:italic> can be roughly associated with the pairing effect, while the differences of <mml:math altimg="si54.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> at adjacent even and odd values of <ce:italic>N</ce:italic> provide information related to the spacing between single-particle levels, that is, information related to the mean-field contribution. The values of <mml:math altimg="si55.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> calculated using the experimental masses tabulated in Ref. <ce:cross-ref refid="bib012">[12]</ce:cross-ref> and the results of the present work are displayed in <ce:cross-ref refid="fig002">Fig. 2</ce:cross-ref><ce:float-anchor refid="fig002"/> as a function of neutron number for four isotopic chains. Let us first consider the case of Ca isotopes (<mml:math altimg="si56.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math>). As the difference between <mml:math altimg="si57.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> evaluated at adjacent neutron numbers is sensitive to the single-particle energy differences, it peaks at the magic numbers <mml:math altimg="si58.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28. The <mml:math altimg="si59.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> is almost constant between <mml:math altimg="si60.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28 because, for spherical nuclei, the single-particle energy is constant within a shell. At <mml:math altimg="si61.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi></mml:math> a strong jump in the <mml:math altimg="si62.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> is observed for all nuclei, and can be attributed to the Wigner term (see, for example, Ref. <ce:cross-ref refid="bib015">[15]</ce:cross-ref>). The Si isotopes (<mml:math altimg="si63.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:math>) show a very similar behavior to that of Ca between <mml:math altimg="si64.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 27, which indicates a regular filling of the <mml:math altimg="si65.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>7</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> orbital. On the contrary, the behavior of the P (<mml:math altimg="si66.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>15</mml:mn></mml:math>) and S (<mml:math altimg="si67.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:math>) chains is different from that of Ca. A local maximum appears at <mml:math altimg="si68.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math> rather than at <mml:math altimg="si69.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math>. Such an effect at <mml:math altimg="si70.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math> was already observed in our previous measurement and was attributed to deformation <ce:cross-ref refid="bib010">[10]</ce:cross-ref>. Owing to the reduction in the uncertainties in the masses for the most neutron-rich P and S isotopes, the effect at <mml:math altimg="si71.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math> and the vanishing of <mml:math altimg="si72.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> as a shell closure have become considerably more apparent than in Ref. <ce:cross-ref refid="bib010">[10]</ce:cross-ref>. Moreover, the present data clearly show that there is no such effect at <mml:math altimg="si73.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math> for the Si isotopes.</ce:para><ce:para view="all">Apart from the effects of deformation, an erosion of the <mml:math altimg="si74.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> shell closure could also result from a decrease in the spin–orbit interaction far from stability <ce:cross-ref refid="bib016">[16]</ce:cross-ref>. The case of <ce:sup loc="pre">42</ce:sup>Si is of particular interest as it could be stabilized against deformation by the <mml:math altimg="si75.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:math> sub-shell closure. Interestingly, the theoretical predictions for this nucleus are rather contradictory. On the one hand, shell model calculations suggest that <ce:sup loc="pre">42</ce:sup>Si has the characteristics of a doubly-magic nucleus such as <ce:sup loc="pre">48</ce:sup>Ca <ce:cross-ref refid="bib017">[17]</ce:cross-ref>. The same conclusion was reached in Ref. <ce:cross-ref refid="bib018">[18]</ce:cross-ref>, where the deformed configuration was found to be located 1 MeV above the ground state, whereas in other <mml:math altimg="si76.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> nuclei (such as <ce:sup loc="pre">40</ce:sup>Mg) the deformed intruder state is well below the closed shell. On the other hand, relativistic Hartree–Bogoliubov calculations predict a strong oblate deformed configuration for <ce:sup loc="pre">42</ce:sup>Si <ce:cross-ref refid="bib019">[19]</ce:cross-ref>, in agreement with relativistic mean field calculations with BCS pairing (RMF-BCS) <ce:cross-ref refid="bib020">[20]</ce:cross-ref> and with the results of the latest version of the Skyrme–Hartree–Fock–Bogoliubov (HFB-9) model <ce:cross-ref refid="bib021">[21]</ce:cross-ref>. While Refs. <ce:cross-ref refid="bib019">[19]</ce:cross-ref> and <ce:cross-ref refid="bib020">[20]</ce:cross-ref> predict a rapid transition from prolate to oblate deformation at <mml:math altimg="si77.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math>, for HFB-9 <ce:cross-ref refid="bib021">[21]</ce:cross-ref> this sudden change in deformation arises at <mml:math altimg="si78.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math>, that is, when going from <ce:sup loc="pre">41</ce:sup>Si to <ce:sup loc="pre">42</ce:sup>Si. From the experimental point of view the situation is rather unclear as well. Grévy et al. have measured the <ce:italic>β</ce:italic>-decay half-lives of several Si isotopes <ce:cross-ref refid="bib022">[22]</ce:cross-ref>. The short half-life of <ce:sup loc="pre">42</ce:sup>Si could only be reproduced theoretically assuming a strongly deformed configuration. The present mass measurements of the most neutron-rich Si isotopes are important in order to confirm the conclusions of <ce:cross-ref refid="bib022">[22]</ce:cross-ref>, because the <mml:math altimg="si79.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>Q</mml:mi><mml:mi>β</mml:mi></mml:msub></mml:math> influences to the fifth power the lifetime. Contrary to the conclusions of Ref. <ce:cross-ref refid="bib022">[22]</ce:cross-ref>, high-energy two-proton removal cross sections populating <ce:sup loc="pre">42</ce:sup>Si from a <ce:sup loc="pre">44</ce:sup>S beam were interpreted as a signature of the doubly magic character of <ce:sup loc="pre">42</ce:sup>Si <ce:cross-ref refid="bib023">[23]</ce:cross-ref>. However, in a more recent article it was recognized that the two-proton knockout cross section populating <ce:sup loc="pre">42</ce:sup>Si is not sensitive to the size of the <mml:math altimg="si80.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> gap <ce:cross-ref refid="bib024">[24]</ce:cross-ref>. The mass of <ce:sup loc="pre">42</ce:sup>Si can clearly aid in shedding new light on this question. From the mass measured in the present work one-neutron separation energies of <mml:math altimg="si81.gif" display="inline" overflow="scroll"><mml:mn>5.03</mml:mn><mml:mo>±</mml:mo><mml:mn>0.69</mml:mn><mml:mtext> </mml:mtext><mml:mtext>MeV</mml:mtext></mml:math> (<ce:sup loc="pre">42</ce:sup>Si) and <mml:math altimg="si82.gif" display="inline" overflow="scroll"><mml:mn>4.96</mml:mn><mml:mo>±</mml:mo><mml:mn>0.24</mml:mn><mml:mtext> </mml:mtext><mml:mtext>MeV</mml:mtext></mml:math> (<ce:sup loc="pre">40</ce:sup>Si) were obtained. For the even Si-isotopes, the tabulated <mml:math altimg="si83.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> decreases by about 1 MeV when going to the next even isotope. One would then expect an <mml:math altimg="si84.gif" display="inline" overflow="scroll"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> of about 4 MeV for <ce:sup loc="pre">42</ce:sup>Si. Our results thus suggest a possible increase in binding as would be expected from a shell closure. <ce:cross-ref refid="fig003">Fig. 3</ce:cross-ref><ce:float-anchor refid="fig003"/> represents the microscopic energy as a function of neutron number for the same isotopic chains as in <ce:cross-ref refid="fig002">Fig. 2</ce:cross-ref>. The microscopic energy, a convenient quantity to inspect the presence of structure effects in nuclear masses, has been obtained by subtracting the macroscopic component (as given by the Finite Range Liquid Drop Model FRLDM <ce:cross-ref refid="bib025">[25]</ce:cross-ref>) from the experimental mass excess. The variation of the microscopic energy as a function of neutron number should exhibit deep minima at the shell closures. In <ce:cross-ref refid="fig003">Fig. 3</ce:cross-ref> a strong change in slope at <mml:math altimg="si85.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and near <mml:math altimg="si86.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> can be observed for <mml:math altimg="si87.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math>. However, the <mml:math altimg="si88.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>15</mml:mn></mml:math> and <mml:math altimg="si89.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:math> isotopes do not show such features at <mml:math altimg="si90.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> and present instead a discontinuity in the slope at <mml:math altimg="si91.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:math>, as observed in our earlier work <ce:cross-ref refid="bib010">[10]</ce:cross-ref>. This discontinuity is absent for the <mml:math altimg="si92.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:math> isotopes. The similar behavior of the microscopic energy for <mml:math altimg="si93.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:math> and 20 could be considered evidence of a shell closure at <mml:math altimg="si94.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math>, in agreement with the discussion of the OES above. However, in a recent <ce:italic>γ</ce:italic>-spectroscopy experiment <ce:cross-ref refid="bib026">[26]</ce:cross-ref> evidence for a low lying <mml:math altimg="si95.gif" display="inline" overflow="scroll"><mml:msup><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:math> state in <ce:sup loc="pre">42</ce:sup>Si was found, which is not compatible with such a picture. All these observations could be consistent, however, if deformation effects appear suddenly at <mml:math altimg="si96.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math>.</ce:para><ce:para view="all">Reliable mass formulas that permit extrapolations to the unknown regions of the nuclear chart are important for many domains, such as nuclear astrophysics, and many mass formulas have been developed in recent years <ce:cross-ref refid="bib027">[27]</ce:cross-ref>. Our results provide new data to test the predictive power of different mass formulas when approaching the neutron dripline. In <ce:cross-ref refid="fig004">Fig. 4</ce:cross-ref><ce:float-anchor refid="fig004"/> we have compared our experimental values of <mml:math altimg="si98.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> for the Si isotopic chain with the HFB-9 mass formula <ce:cross-ref refid="bib021">[21]</ce:cross-ref>, the Duflo–Zuker formula <ce:cross-ref refid="bib028">[28]</ce:cross-ref>, and with the RMF-BCS model <ce:cross-ref refid="bib020">[20]</ce:cross-ref>. One can see that the best description is given by the Duflo–Zuker formula. This is also true for the other isotopic chains, in agreement with <ce:cross-ref refid="bib027">[27]</ce:cross-ref>. The HFB-9 model does, for example, not reproduce the shell closure at <mml:math altimg="si99.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and, indeed, for <mml:math altimg="si100.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>21</mml:mn></mml:math> and 22 it overpredicts the mass. For <mml:math altimg="si101.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>></mml:mo><mml:mn>22</mml:mn></mml:math> the differences between the HFB-9 mass formula and the data decrease. The values of <mml:math altimg="si102.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> for odd-<ce:italic>N</ce:italic> derived from the RMF-BCS calculations are systematically lower than the experimental results, probably owing to a weak pairing strength. The predictive power of this model could, therefore, be greatly improved by utilizing a better parametrization of the pairing. The rms value of the differences between the masses listed in <ce:cross-ref refid="tbl001">Table 1</ce:cross-ref> and the predictions of the FRLDM is 2.721 MeV, for the Duflo–Zuker formula 0.777 MeV, for HFB-9 1.11 MeV, and 1.73 MeV for the RMF-BCS model.</ce:para><ce:para view="all">Finally, our results have also been employed to derive a new shell-model parametrization for the s-d shell Hamiltonians, called USDA and USDB. As a result, a better agreement with experiment for binding energies and excitation energies in the region of <ce:sup loc="pre">24</ce:sup>O has been found, with a reduction of the rms deviation to around 0.13 MeV <ce:cross-ref refid="bib029">[29]</ce:cross-ref>.</ce:para><ce:para view="all">In conclusion, we have determined using a direct time-of-flight technique the masses of a broad range of neutron-rich nuclei situated in the vicinity of the <mml:math altimg="si103.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:math> and 28 shell closures. The masses of 7 nuclei have been measured for the first time and the precisions of 36 masses have been considerably improved, in many cases by more than a factor two. These results have been used to explore the evolution of the OES with neutron number, whereby we observe a clear reduction of the OES as the one-neutron separation energy decreases for the <mml:math altimg="si104.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn><mml:mo>,</mml:mo><mml:mn>10</mml:mn></mml:math> and 12 isotopic chains. This effect needs to be carefully interpreted in order to establish the relative importance of pairing, spin–isospin coupling, and coupling to the continuum which may be needed to explain the observed behavior. Our results also corroborate the changes in shell structure already observed for the P and S isotopes at the <mml:math altimg="si105.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> shell closure. In contrast, such effects are seen to be absent for the Si isotopes. This could indicate either the persistence of the <mml:math altimg="si106.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math> shell closure for the Si isotopes, or it may reflect a very sudden change in deformation at <mml:math altimg="si107.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:math>, as predicted by Ref. <ce:cross-ref refid="bib021">[21]</ce:cross-ref>. To answer this question, <ce:sup loc="pre">42</ce:sup>Si and neighboring neutron-rich nuclei need to be further investigated. Finally, our results have been used to test and suggest improvements to various mass models as well as derive an improved shell model interaction.</ce:para></ce:sections><ce:acknowledgment><ce:section-title>Acknowledgements</ce:section-title><ce:para view="all">The authors would like to thank M. Yamagami for fruitful discussions and L. Gaudefroy for carefully reading the manuscript. 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