application/xmlShell structure beyond the proton drip line studied via proton emission from deformed 141HoM. KarnyK.P. RykaczewskiR.K. GrzywaczJ.C. BatchelderC.R. BinghamC. GoodinC.J. GrossJ.H. HamiltonA. KorgulW. KrólasS.N. LiddickK. LiK.H. MaierC. MazzocchiA. PiechaczekK. RykaczewskiD. SchapiraD. SimpsonM.N. TantawyJ.A. WingerC.H. YuE.F. ZganjarN. NikolovJ. DobaczewskiA.T. KruppaW. NazarewiczM.V. StoitsovProton radioactivityProton shell structureTwo-body tensor interactionsPhysics Letters B 664 (2008) 52-56. doi:10.1016/j.physletb.2008.04.056journalPhysics Letters BCopyright © 2008 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26936641-212 June 20082008-06-1252-56525610.1016/j.physletb.2008.04.056http://dx.doi.org/10.1016/j.physletb.2008.04.056doi:10.1016/j.physletb.2008.04.056http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/

Journals

S300.2

PLB24902S0370-2693(08)00518-210.1016/j.physletb.2008.04.056Elsevier B.V.Experiments

Fig. 1

The energies of decay signals within 1–16 ms after the implantation of 141Ho ions. An energy difference of 201(6) keV was obtained for two observed proton peaks, the known transition at 1169(8) keV [13] and the peak at 0.97 MeV corresponding to a proton transition to the 202.1 keV 2+ level in 140Dy [16].

Fig. 2

(a) Energy spectrum of Ho141m decay signals between 0.5 and 40 μs after the recoil implantation. The energy difference of 204(11) keV between two observed peaks was determined using the calibration procedure based on the known 959.7(28) keV proton line from 113Cs [26,27] and verified using known 1235(9) keV Ho141m proton peak [15]. Shaded areas correspond to the energy gates used in the lifetime analysis. The 1.17 MeV proton emission from 4.1 ms Ho141gs resulted in about 20 counts present in the spectrum at the left side of the 1235 keV line. Panel (b) shows the decay pattern of the main peak together with the exponential fit yielding a more precise value of T1/2=7.4(3) μs microseconds for Ho141m. (c) Decay pattern of the 1.03 MeV line (horizontally hashed) together with predicted shape for the T1/2=7.4 μs decay.

Fig. 3

Comparison between experimental (⋆; from [18]) and calculated (SLy4, SkM∗, and SkP HFB models [35,36]; HFB14 [40]; FRDM [41]) quadrupole deformations of even–even Dy isotopes with 74⩽N⩽102. Results of the global best fit of Ref. [18] are also shown (open stars). The oblate-prolate energy difference calculated in the SLy4+HFB model for even–even Sm, Gd, and Dy isotopes around N=76 is shown in the inset.

Fig. 4

The impact of tensor interaction on single-proton canonical states in the Holmium isotopes with 70⩽N⩽102. Upper panel: energy difference between 2f7/2 and 1h11/2 levels. Lower panel: energy difference between 2d3/2 and 3s1/2 levels. Calculations were carried out within the spherical HFB approach without (SkO) and with (SkOT) inclusion of the two-body tensor interaction [51].

Shell structure beyond the proton drip line studied via proton emission from deformed 141Ho

Karny

⁎

karny@mimuw.edu.pl

K.P.

Rykaczewski

R.K.

Grzywacz

J.C.

Batchelder

C.R.

Bingham

Goodin

C.J.

Gross

J.H.

Hamilton

Korgul

Królas

S.N.

Liddick

K.H.

Maier

Mazzocchi

Piechaczek

Rykaczewski

Schapira

Simpson

M.N.

Tantawy

J.A.

Winger

C.H.

E.F.

Zganjar

Nikolov

Dobaczewski

A.T.

Kruppa

Nazarewicz

M.V.

Stoitsov

aInstitute of Experimental Physics, Warsaw University, Warsaw, PL 00681, PolandbJoint Institute for Heavy Ion Research, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAcPhysics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAdDepartment of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USAeUNIRIB/Oak Ridge Associated Universities, Oak Ridge, TN 37831, USAfDepartment of Physics, Vanderbilt University, Nashville, TN 37235, USAgInstitute of Nuclear Physics, Kraków, PL 31342, PolandhIFGA, University of Milan and INFN, Milano, I-20133, ItalyiDepartment of Physics, Louisiana State University, Baton Rouge, LA 70803, USAjWoodruff School of Mechanical Engineering, Georgia Institute of Technology, GA 30332, USAkDepartment of Physics, Mississippi State University, Mississippi State, MS 39762, USAlInstitute of Theoretical Physics, Warsaw University, Warsaw, PL 00681, PolandmDepartment of Physics, University of Jyväskylä, FI-40014, FinlandnInstitute of Nuclear Research, Bem tér 18/c, 4026 Debrecen, HungaryoInstitute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria⁎Corresponding author at: Institute of Experimental Physics, Warsaw University, PL 00681 Warsaw, Hoża 69, Poland.

Editor: V. Metag

Abstract

Fine structure in proton emission from the 7/2−[523] ground state and from the 1/2+[411] isomer in deformed nucleus 141Ho was studied by means of fusion-evaporation reactions and digital signal processing. Proton transitions to the first excited 2+ state in 140Dy, with the branching ratio of Ipgs(2+)=0.9±0.2% and Ipm(2+)=1.7±0.5%, were observed. The data are analyzed within the non-adiabatic weak coupling model assuming a large quadrupole deformation of the daughter nucleus 140Dy as predicted by the self-consistent theory. Implications of this result on coexistence effects around N=74 are discussed. Significant modifications of the proton shell structure when going from the valley of beta stability to the proton drip line are discussed in terms of self-consistent theory involving the two-body tensor interaction.

Keywords

Proton radioactivityProton shell structureTwo-body tensor interactions

PACS

23.50.+z21.10.Pc24.10.Eq27.60.+j

Introduction

New experimental advances along the isospin axis require safe and reliable theoretical predictions of nuclear properties throughout the whole nuclear chart. In this context, of particular importance are experimental data for extremely proton-rich and neutron-rich nuclei in which poorly known components of the effective interaction, in particular in the spin-isospin channel, are amplified. The isospin dependence of the effective interaction and the presence of states that are unbound to particle-emission may have significant impact on spectroscopic properties of nuclei, e.g., variations in the single-particle (s.p.) shell structure [1].Theoretical predictions and experimental discoveries in the last decade indicate that nucleonic shell structure is being recognized now as a more local concept [2–4]. In this context, a lot of attention has been given to neutron-rich nuclei where spectacular changes in the neutron shell structure have been seen, including the disappearance and emergence of magic gaps [5]. So far, there have been no strong indications of appreciable variations of the proton shell structure in proton-rich nuclei. The usual explanation is given in terms of the confining effect of the Coulomb barrier that (i) leads to spatial localization of narrow resonances above the proton emission threshold, and (ii) effectively shifts the non-resonant proton continuum up in energy. While many-body correlations in proton-rich systems are not going to be very different compared to stable nuclei, and the threshold effects are much less significant than on the neutron-rich side, one can certainly expect changes in the effective interaction when moving from the stability valley towards the proton drip line. To put things in perspective, the stable Ho isotope, Ho9867165 (T=31/2), contains 24 more neutrons as compared to the proton emitter Ho7467141 (T=7/2) discussed in this work. The corresponding change in the neutron shell structure implies appreciable variation in spin saturation, and this is expected to impact the tensor components of the interaction; hence spin-orbit fields [6–8].Proton emitters are spectacular examples of open quantum systems and a wonderful playground to study coupling between bound and unbound nuclear states. Proton emitters also provide a wealth of spectroscopic information on proton and neutron shell structure in proton-rich nuclei. Measured proton energies, lifetimes, and proton branching ratios (fine structure) allow us to deduce the angular momentum of the emitted proton and to characterize its wave function inside the nucleus [9–12]. This, together with properties of collective states in neighboring nuclei, enables theory to fine-tune nuclear structure models.This Letter presents the first observation of fine structure in proton emission from two states in an odd-Z, even-N nucleus: the 7/2−[523] ground-state and 1/2+[411] isomeric state in deformed 141Ho. The measured decay properties are used to extract information on the wave functions of these unbound deformed Nilsson levels and on the proton mean field in this region.The discovery of the proton-emitting ground state of 141Ho (T1/2=4.2(4) ms, Ep=1169(8) keV) [13] was followed by the observation of proton emission from a short-lived isomeric state (T1/2=8(3) μs, Ep=1230(20) keV) at about 60 keV excitation energy [14]. The deformed Nilsson orbitals 7/2−[523] and 1/2+[411] were assigned to Ho141gs[13] and Ho141m[14], respectively. In a subsequent experiment [15], rotational bands built upon these deformed bandheads were identified. The experimental upper limit for the fine structure branching ratio I(21+) was quoted as 1% for both ground- and isomeric state assuming the energy of the rotational 21+ state in 140Dy to be ⩽250 keV[15]. The 21+ energy was later measured in Refs. [16,17] to be 202.2(1) keV suggesting a quadrupole deformation β2≈0.23–0.24[18], and thus making 141Ho, together with 131Eu [19], a paradigm for a proton emission from a deformed nucleus.2

Experiment

The ions of Ho141gs and Ho141m ions were produced at ORNL's HRIBF using fusion-evaporation reactions with a 20–35 particle nA 54Fe beam impinging on a 92Mo target. Beam energies of 300 MeV and 290 MeV were optimized for target thicknesses of 1.0 and 0.6 mg/cm2, respectively. Reaction products were separated according to their mass-to-charge ratio, A/Q=141/25 and 141/26 by the Recoil Mass Spectrometer (RMS) [20]. RMS-selected recoils were implanted into a 65-microns thick Double-sided Silicon Strip Detector (DSSD, FWHM=18–25 keV for Ep=1.17 MeV) after passing trough a thin-foil, position-sensitive Micro Channel Plate (MCP) detector and being slowed down to about 60–70 MeV by a degrader foil. The flight time through the separator was 2.2 μs. The production cross sections were evaluated to be 1.4 μb at 300 MeV and 240 nb at 290 MeV for Ho141gs and Ho141m, respectively, at the RMS transmission of 5%. In the first 90-hour experiment on Ho141gs, the DSSD was backed with a 0.5-mm thick Si detector (FWHM=75 keV for Eα=5.5 MeV). The signals from all detectors were read by the Digital Gamma Finder (DGF) modules [21] and analyzed on-board. The Ho141gs proton transition of 1169(8) keV [13] was used to establish the offset-free energy calibration of proton induced signals analyzed in the digital detection system [21]. The energy spectra of emitted protons were obtained using time and pixel correlations with implanted ions, requesting an energy difference below ±4% for the coincidence signals recorded in the front and back DSSD strips [22], and requiring an anticoincidence condition with the Si detector behind the DSSD. For the Ho141m measurement (85 hours with a steady 35 particle nA 54Fe beam), four 0.7-mm thick Si detectors forming sides of a box upstream of the DSSD (Si-box) detecting the DSSD-escaping protons were added, and a 4-mm thick Si(Li) detector replaced the 0.5-mm Si counter [23]. The signals counted by the Si-box detectors (FWHM=60 keV for Eα=5.5 MeV) and Si(Li) detector (FWHM=120 keV for Eα=5.5 MeV) were used to veto the DSSD-recorded energy spectra and allowed us to reduce substantially the background below the main Ho141m proton peak, compare [24]. Due to the short half-life of Ho141m, the DGF modules serving the DSSD were programmed to trigger only for events where the recoil implantation signal was followed by the decay within the 0.5–40 μs time range (“proton-catcher” mode [25]). The waveforms (traces) containing both recoil and decay signals were stored for further analysis. For the sake of analysis of Ho141m data, a database of normalized single pulse reference traces was constructed. A full range trace fit, with two reference traces (for recoil and decay) and a constant baseline, was performed for each event. Scaling factors for both traces are free parameters of the fit and are proportional to the energy deposited by the heavy ion or proton in the DSSD. The offset-free energy calibration was performed using the Ep=959.7(28) keV protons [26] from 113Cs decay (T1/2=18.3(3) μs[27]) and verified using the main 1235(9) keV proton transition from Ho141m[15], see [24] for more details.

Fig. 1

shows the energy spectrum of Ho141gs decay signals between 1 ms and 16 ms after recoil implantation. Apart from the main peak and the proton escape events, a peak at the energy of 0.97 MeV was detected. The energy difference of 201(6) keV between the main peak and the satellite one is consistent with the energy of the 21+ state in 140Dy. The peak areas of 57(12) and 6360(80) counts in the satellite and main peak, respectively, yield the branching ratio Ipgs(21+)=0.9(2)% for proton emission from Ho141gs. One-component exponential fit to the decay pattern of the main peak gives a more precise half-life value of 4.1(1) ms for Ho141gs. The energy spectrum of Ho141m decay events within 40 μs after ion implantation is presented in Fig. 2

(panel (a)). Panel (b) shows the decay pattern of the main peak together with the exponential fit yielding value of T1/2=7.4(3) μs for Ho141m. The time distribution of satellite peak events is consistent with the half-life of 7.4 μs (panel (c)). The proton energy of 1.03(1) MeV agrees very well with the energy expected for the decay to the 2+ excited state. On the basis of the observed half-life and energy, we assign the satellite peak to the proton transition from the Ho141m state to the first 2+ excited state in 140Dy. With 13 counts above the background of 4 counts for the satellite peak and 770(30) counts in the main peak the branching ratio for this transition was calculated to be Ip(2+)=1.7(5)%.

Discussion

Decay properties of 141Ho have been discussed in a number of theoretical approaches, differing in degree of sophistication [11,28–30]. Up to now, none of the theoretical approaches employed was able to explain all measured properties related to the structure and decay of 141Ho and Ho141m, including lifetimes, branching ratios, and ordering of single-particle levels. This should not come as a surprise as decay properties of 141Ho depend crucially on small components in the wave function that sensitively depend on the choice and magnitude of couplings considered. Namely, the lifetime of 141Ho is governed by a small πf7/2⊗0+ component of the g.s. wave function of predominantly h11/2 character. The increase in the πf7/2 amplitude is immediately reflected by a faster proton emission. On the other hand, the decay of Ho141m to Dy140gs solely depends on a πs1/2⊗0+ component, while the transition to the 21+ state (hence the branching ratio Ipm(21+)) depends on πd3/2⊗21+ and πd5/2⊗21+ partial widths (the s1/2 wave is excluded by virtue of angular momentum conservation).Proton emission calculations have been carried out within the non-adiabatic weak coupling model [31,32] in the recent variant based on the combination of the R-matrix theory and the oscillator expansion technique [11] that allows for a substantial increase of the number of coupled channels. We employed the same successful Chepurnov parameterization [33] of the Woods–Saxon (WS) optical potential as earlier in Ref. [32]. Compared to our earlier studies, we now consider the full deformed spin–orbit (s.o.) potential. (See Ref. [34] for the definition of the average deformed Hamiltonian.) The inclusion of deformation in the s.o. potential improves the description of the deformed [411]3/2+ proton-emitting Eu131gs measured to have T1/2p=26.6(4) ms and Ipgs(21+)=24(5)%[19]. Assuming a spherical s.o. potential, one obtains T1/2=34 ms and Ipgs(21+)=39%[32], while our improved calculations give T1/2=18 ms and Ipgs(21+)=20% taking the BCS spectroscopic factor u2=0.67.Many structural properties of 141Ho, including its spectrum and decay, depend on its shape deformation. While there is a consensus regarding the large elongation of this system, there is a considerable uncertainty regarding the actual value of quadrupole deformation β2 of 141Ho and its core 140Dy. Fig. 3

shows predicted values of |β2| for even–even Dy isotopes with 74⩽N⩽102 obtained in several theoretical models: Hartree–Fock–Bogoliubov (HFB) mass models of Refs. [35,36] with SLy4 [37], SkM∗[38], and SkP [39] density functionals, the recent HFB14 mass model [40], and the Finite-Range Droplet Model (FRDM) [41]). For nuclei with N>84, experimental information on β2 exists from B(E2)↑ rates[18]; these values agree well with the global expression of Ref. [18], β2=(466±41)E2+−1/2/A, representing systematic trends. For nuclei close to the stability line, theory does fairly well, with FRDM slightly underestimating experiment and HFB14 being on the high side. The situation becomes less clear for neutron-deficient nuclei with N<82. For N=74, all HFB models predict a strongly deformed prolate shape with β2 ranging from 0.34 (SkP, SkM∗) to 0.41 (HFB14). The FRDM value is again reduced as compared to HFB models, β2=0.27, while the global fit yields β2≈0.23. The difference between the phenomenological expression and HFB calculations is rather surprising, considering the excellent agreement for heavier nuclei. In order to explain this puzzle, we first note that theory predicts a coexistence between prolate and oblate shapes in this region. The inset in Fig. 3 shows the oblate-prolate energy difference calculated in the SLy4+HFB model for even–even Sm, Gd, and Dy isotopes with 72⩽N⩽80. While N=72 and 74 isotopes are predicted to be prolate, a transition to an oblate configuration with β2≈−0.2 is expected at N=76. A similar result has been obtained in SkM∗, SkP, and HFB11 models, as well as in FRDM and NL–SH models [42] where, however, the transition to oblate shapes occurs at N=78.

Coexistence between low-lying well-deformed prolate and less-deformed oblate configurations may be the reason for an unexpectedly large energy of the 21+ state in 140Dy and a pronounced steady increase in the moment of inertia of this nucleus up to Jπ=8+. Interestingly, a low-lying, even-spin, positive-parity excited band has been found in the lighter N=74 isotones of 136Sm [43] and 138Gd [44]. While this structure has been interpreted as a γ band, its reduced alignment and irregular behavior at low spins are not inconsistent with a coexisting configuration. The influence of triaxiality on Ho141gs decay was studied in Refs. [11,28], and it was concluded that coupling to γ-vibrational states was not able to explain the experimental data.In view of the above discussion, we adopted the HFB deformation β2=0.35 and β4=−0.05 for the coupled channel calculations. At this deformation, the [523]7/2− and [411]1/2+ levels are nearly degenerate and appear at the Fermi level of Z=67. (A similarly large prolate deformation has been predicted in Ref. [45] based on the relativistic mean field theory.) With this prolate shape, taking the BCS values u2([523]7/2−)=0.84 and u2([411]1/2+)=0.81, our calculations give T1/2=7.8 ms (I(21+)=1.3%) and T1/2=7.6 μs (I(21+)=1%) for 141Ho and Ho141m, respectively. The resulting g.s. wave function of 141Ho g.s. is dominated by the h11/2 component (78.2%); the total f7/2 amplitude is 12.6%. This can be compared to 81% of h11/2 and 11.5% of f7/2 obtained at β2=0.29 (and spherical s.o. potential) in [32]. The isomeric state Ho141m is predicted to be strongly mixed, with 6.7% of s1/2 component. This can be compared to 11% of s1/2 parentage in the previous version of our model.While the reproduction of the data is quite fair, further refinements of the model are possible. They include: (i) inclusion of coupling with coexisting oblate (or triaxial) configuration in 140Dy along the lines of Ref. [46]; (ii) inclusion of pairing interaction in the weak coupling approach (see Refs. [30,47] for treatment of pairing within the strong coupling scheme); and (iii) considering a more realistic optical model potential. The latter point is particularly important as the relative positions of s.p. levels can strongly impact amplitudes of small components of the wave function of the parent nucleus that govern proton emission.Microscopically, significant variations of s.p. states with shell filling can be caused by the two-body tensor force that is sensitive to the effect of spin saturation. On a one-body level, variation of the phenomenological s.o. potential due to the tensor force was studied in the 1980s by either considering an average tensor contribution to the s.o. term [48] or by phenomenologically changing the s.o. strength with shell filling [49]. It is only very recently, stimulated by the new data on neutron-rich nuclei, that the self-consistent treatment of the effective tensor interactions has been reintroduced [6–8].In order to examine the effect of the two-body tensor force on s.p. states of rare earth nuclei, we carried out spherical self-consistent HFB calculations with the SkO functional [50] with and without the tensor term [51]. The relative energies of 2f7/2 and 1h11/2 proton orbitals (determining the 141Ho g.s. decay), and 2d3/2 and 3s1/2 (determining the Ho141m decay) are displayed in Fig. 4

as a function of neutron number. In both cases, inclusion of the tensor term produces an appreciable contribution to the splitting between crucial spherical shells when moving away from the line of beta stability towards the proton drip line. Moreover, the self-consistent mechanism present in the HFB results produces enhanced variations as compared to the WS model. Namely, the 2d3/2–3s1/2 splitting of WS energies changes only by 20 keV when going from 165Ho to 141Ho.

In summary, decay properties of 7/2− and 1/2+ states in deformed 141Ho have been reinvestigated yielding more accurate half-life values of 4.1(1) ms and 7.4(3) μs, respectively. For the first time in proton radioactivity studies, fine structure in proton emission from different levels in the odd-Z, even-N parent nucleus was detected, with branching ratios of 0.9(2)% (7/2−) and of 1.7(5)% (1/2+). The structure of proton-emitting states was reanalyzed using an improved non-adiabatic approach. Good agreement with experimental data was obtained without changing any parameter values but taking the increased quadrupole deformation as predicted by the self-consistent theory. The large deformation of 140Dy (also used in [29]) is consistent with the known proton shell structure around Z=67. The apparent deviation from systematic trends at N=74 might be caused by coexistence effects predicted in this region by several mean-field approaches. To clarify the puzzle of abnormally large 21+ energy, lifetime measurements for the low-spin yrast states of 140Dy and a search for an excited collective band in this nucleus are required.Finally, using the self-consistent HFB theory, we investigated the neutron number dependence of single-proton states in the Ho isotopes. We found significant variations of proton shell structure with neutron number. The changes are caused by both the self-consistency mechanism and the two-body tensor force that significantly impacts the s.p. splitting. This result indicates a direction for future theoretical refinements of our model.

Acknowledgement

ORNL is managed by UT-Battelle, LLC, for the US Department of Energy under Contract DE-AC05-00OR22725. This work was also supported by the US DOE through Contract Nos. DE-FG02-96ER40983, DE-FG02-96ER40963, DE-FC02-07ER41457, DE-FG02-96ER41006, DE-FG05-88ER40407, DE-FG02-96ER40978, and DE-AC05-76OR00033; by the National Nuclear Security Administration through DOE Research Grant DE-FG03-03NA00083; by the Polish Ministry of Science; by the Foundation for Polish Science (A.K.); by the Academy of Finland and University of Jyväskylä within the FIDIPRO program; and by Hungarian OTKA grant No. T46791.

References

[1]

Dobaczewski

Michel

Nazarewicz

Płoszajczak

RotureauProg. Part. Nucl. Phys.

2007

432

[2]

Dobaczewski

NazarewiczPhilos. Trans. R. Soc. London A

356

1998

2007

[3]

R.F.

Casten

B.M.

SherrillProg. Part. Nucl. Phys.

2000

S171

[4]

D.F.

Geesaman

Annu. Rev. Nucl. Part. Sci.

2006

[5]

R.V.F.

JanssensNature

435

2005

[6]

Dobaczewski

nucl-th/0604043

[7]

Otsuka

Matsuo

AbePhys. Rev. Lett.

2006

162501

Dobaczewski

Duguet

Esbensen

K.M.

Nollet

C.D.

RobertsProceedings of the Third ANL/MSU/INT/JINA RIA Theory Workshop: Opportunities with Exotic BeamsArgonne, USA, 4–7 April, 20062007World ScientificSingapore

152

nucl-th/0604043

[8]

B.A.

Brown

Phys. Rev. C

2006

061303(R)

[9]

P.J.

Woods

C.N.

DavidsAnnu. Rev. Nucl. Part. Sci.

1997

541

[10]

A.A.

SonzogniNucl. Data Sheets

2002

[11]

A.T.

Kruppa

NazarewiczPhys. Rev. C

2004

054311

[12]

L.S.

Ferreira

M.C.

Lopes

MaglioneProg. Part. Nucl. Phys.

2007

418

[13]

C.N.

Davids

Phys. Rev. Lett.

1998

1849

[14]

Rykaczewski

Phys. Rev. C

1999

011301

[15]

Seweryniak

Phys. Rev. Lett.

2001

1458

[16]

Królas

Phys. Rev. C

2002

031303R

[17]

Cullen

Phys. Lett. B

529

2002

[18]

Raman

C.W.

Nestor

TikkanenAt. Data Nucl. Data Tables

2001

[19]

A.A.

Sonzogni

Phys. Rev. Lett.

1999

1116

[20]

C.J.

Gross

Nucl. Instrum. Methods A

450

2000

[21]

GrzywaczNucl. Instrum. Methods B

204

2003

649

[22]

K.P.

Rykaczewski

AIP Conf. Proc.

638

2002

149

[23]

M.N.

Tantawy

Phys. Rev. C

2006

024316

[24]

Karny

AIP Conf. Proc.

961

2007

[25]

Karny

Phys. Rev. Lett.

2003

012502

[26]

HofmannRadiochim. Acta

70/71

1995

[27]

C.J.

Gross

AIP Conf. Proc.

455

1998

444

[28]

C.N.

Davids

EsbensenPhys. Rev. C

2004

034314

[29]

L.S.

Ferreira

MaglioneJ. Phys. G

2005

S1569

[30]

Volya

DavidsEur. Phys. J. A

2005

s01

161

[31]

A.T.

Kruppa

Phys. Rev. Lett.

2000

4549

[32]

Barmore

Phys. Rev. C

2000

054315

[33]

V.A.

ChepurnovYad. Fiz.

1967

955

[34]

Ćwiok

Comput. Phys. Commun.

1987

379

[35]

M.V.

Stoitsov

Phys. Rev. C

2003

054312

[36]

Dobaczewski

Stoitsov

NazarewiczAIP Conf. Proc.

726

2004

[37]

Chabanat

Nucl. Phys. A

635

1998

231

[38]

Bartel

Nucl. Phys. A

386

1982

[39]

Dobaczewski

Flocard

TreinerNucl. Phys. A

422

1984

103

[40]

Goriely

Samyn

J.M.

PearsonPhys. Rev. C

2007

064312

[41]

Möller

At. Data Nucl. Data Tables

1995

185

[42]

G.A.

Lalazissis

M.M.

Sharma

RingNucl. Phys. A

597

1996

[43]

E.S.

Paul

J. Phys. G

1993

861

[44]

E.S.

Paul

J. Phys. G

1994

751

[45]

Geng

Toki

MengProg. Theor. Phys.

112

2004

603

[46]

J.D.

Richards

Phys. Rev. C

1997

1389

[47]

Fiorin

Maglione

L.S.

FerreiraPhys. Rev. C

2003

054302

[48]

Płoszajczak

M.E.

FaberZ. Phys. A

299

1981

119

[49]

Dudek

Nazarewicz

WernerNucl. Phys. A

341

1980

253

[50]

P.-G.

Reinhard

Phys. Rev. C

1999

014316

[51]

M. Zalewski, et al., unpublished