The prediction of cross sections for nuclei far off stability is crucial in
the field of nuclear astrophysics. For spherical nuclei close to the dripline
the statistical model (Hauser-Feshbach) approach is not applicable and direct
contributions may dominate the cross sections. For neutron-rich, even-even Sn
targets, we compare the resulting neutron capture cross sections when
consistently taking the input for the direct capture calculations from three
different microscopic models. The results underline the sensitivity of cross
sections calculated in the direct model to nuclear structure models which can
lead to high uncertainties when lacking experimental information.Comment: 4 pages, using espcrc1.sty, Proc. Intl. Conf. "Nuclei in the Cosmos
  IV", Univ. Notre Dame 1996, Nucl. Phys. A, in press. A postscript version can
  also be obtained from http://quasar.physik.unibas.ch/research.htm

Balogh

Dobaczewski

H. Oberhummer

J. Dobaczewski

K.-L. Kratz

Kobos

M. Sharma

Mughabghab

Möller

P. Möller

Rauscher

Sharma

T. Rauscher

Thielemann

Nuclear Physics A

English

arXiv

Rauscher, T.

Kratz, K. L.

Oberhummer, H.

Dobaczewski, J.

Moller, P.

Sharma, M.

edoc

Uncertainties in direct neutron capture calculations due to nuclear structure models

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The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. For spherical nuclei close to the dripline the statistical model (Hauser-Feshbach) approach is not applicable and direct contributions may dominate the cross sections. For neutron-rich, even-even Sn targets, we compare the resulting neutron capture cross sections when consistently taking the input for the direct capture calculations from three different microscopic models. The results underline the sensitivity of cross sections calculated in the direct model to nuclear structure models which can lead to high uncertainties when lacking experimental informationPeer reviewe

Kratz, K.L.

University of Hertfordshire Research Archive

arXiv:nucl-th/9609007v1  2 Sep 19961Uncertainties in direct neutron capture calculations due to nuclearstructure modelsT. Rauschera∗, K.-L. Kratzb, H. Oberhummerc, J. Dobaczewskid, P. Mo¨llere, and M.SharmafaInstitut fu¨r Physik, Universita¨t Basel,Klingelbergstr. 82, CH-4056 Basel, SwitzerlandbInstitut fu¨r Kernchemie, Universita¨t Mainz,Fritz-Strassmann-Weg 2, D-55099 Mainz, GermanycInstitut fu¨r Kernphysik, TU Wien,Wiedner Hauptstr. 8–10, A-1040 Wien (Vienna), AustriadInstitute for Theoretical Physics, Warsaw University,ul. Hoza 69, 00-681 Warsaw, PolandeP. Moller Scientific Computing and Graphics Inc.,Los Alamos, New Mexico, USAfDept. of Physics, Kuwait UniversityKuwait 13060The prediction of cross sections for nuclei far off stability is crucial in the field of nu-clear astrophysics. For spherical nuclei close to the dripline the statistical model (Hauser-Feshbach) approach is not applicable and direct contributions may dominate the crosssections. For neutron-rich, even-even Sn targets, we compare the resulting neutron cap-ture cross sections when consistently taking the input for the direct capture calculationsfrom three different microscopic models. The results underline the sensitivity of crosssections calculated in the direct model to nuclear structure models which can lead to highuncertainties when lacking experimental information.1. INTRODUCTIONExplosive nuclear burning in astrophysical environments produces unstable nuclei whichagain can be targets for subsequent reactions. Most of these nuclei are not accessible interrestrial labs or not fully explored by experiments, yet. For the majority of unsta-ble nuclei the statistical model (Hauser-Feshbach) can be used to determine the crosssections. However, for nuclei close to the dripline the level density becomes too low toapply the statistical model [1] and contributions of a direct interaction mechanism (DI)∗APART fellow of the Austrian Academy of Sciences2Across section (barn)SN-Isotopes DC(30 keV)125 130 135 140 145.0001.001.01Figure 1. Direct-capture cross sections at 30 keV for different Sn isotopes. Levels and masses arecalculated with models by Sharma et al. [3] (triangles), Mo¨ller et al. [4] (dots), and Dobaczewskiet al. [2] (squares). The lines are drawn to guide the eye.AHFB125 130 135 140 145012345678ARMFT124 126 128 130 132 134 136012345678Figure 2. Dependence of level energies on mass number for the even-odd isotopes 125−135Snin the RMFT model [3] (right) and for the isotopes 125−145Sn in the HFB model [2] (left).Shown are the 1/2− state (open circles), the 3/2− state (triangles) and the calculated neutronseparation energy (full circles). The lines are drawn to guide the eye. Note the different rangein mass numbers in the two plots.3may dominate the cross sections. The DI requires the detailed knowledge of energy lev-els (excitation energies, spins, parities), contrary to the statistical model which averagesover resonances. Lacking experimental data, this information has to be extracted frommicroscopic nuclear-structure models.We compare the results for direct neutron capture (calculated in the optical model [6])on the even-even isotopes 124−145Sn with energy levels, masses, and nuclear density dis-tributions taken from different nuclear-structure models. The utilized structure modelswere a Hartree-Fock-Bogoliubov model (HFB) with SkP force [2], a Relativistic MeanField Theory (RMFT) with the parameter set NLSH [3] and a Shell Model based onfolded-Yukawa wave functions (FYSM) [4].A similar study has already been performed for neutron-rich Pb isotopes [5].2. METHODThe cross sections were calculated in the optical model for direct capture [6], utilizingoptical potentials derived by the folding procedure [7]. In the folding approach the nucleartarget density is folded with an energy- and density-dependent effective nucleon-nucleoninteraction in order to obtain the potentials for the bound and scattering states. Onlyone open parameter λ remains which accounts for the effects of antisymmetrization and isclose to unity. The densities required for the determination of the folding potentials wereconsistently calculated from the wave functions of the respective nuclear-structure model.For the bound states the strength parameter λ was fixed by the condition to reproducethe given binding energy of the captured neutron. The value of λ for the scatteringpotential was adjusted to yield the same value of 425 MeV fm3 [8] for the volume integralas determined from the experimental scattering data on stable Sn isotopes [9,10].In order to be able to directly compare the different models, all nuclei were assumed tobe spherical and the spectroscopic factors were set to 1.3. RESULTS AND DISCUSSIONThe results of the calculations for projectiles at Ec.m. = 30 keV are summarized in Fig. 1.For each model we calculated the capture cross section only up to the r-process path. Themost extreme location of the path (farthest away from the line of stability) is determinedby neutron separation energies En ≈ 2 MeV [11]. Depending on the microscopic model,the path will then be located at higher or lower mass numbers A. In the case of RMFT andFYSM it will go through A ≈ 132–134, for HFB the path will be shifted to considerablyhigher mass numbers A ≈ 142–144. (The neutron dripline is also shifted to higher massesin the latter model.)Similar effects as seen in the behavior of the Pb cross sections [5] can also be found forthe Sn cross sections. The cross section can vary by order of magnitudes when going fromone isotope to the next and also differ vastly between the different microscopic models.As the capture to low-spin states (J=1/2, 3/2) accounts for the largest contributions tothe cross section, the results are very sensitive to the presence of bound low-spin states.Since the microscopic models not only yield different masses (i.e. neutron separationenergies) but also exhibit different behaviors of the level energies with changing mass,“jumps” and “gaps” can be seen with some models (RMFT, FYSM), whereas others4(HFB) result in a smoother behavior of the capture cross sections in an isotopic chain.This is illustrated in Fig. 2, which shows the neutron separation energy and the excitationenergy of the 1/2− and 3/2− states in RMFT and HFB. As long as both states are unboundin the RMFT, the cross sections remain low and only jump to higher values when thosestates become bound at the shell closure. As at least the 3/2− level is always bound inHFB, the cross sections show a smoother behavior. The variation in the FYSM crosssections can be explained in a similar way.4. CONCLUSIONWith this work we have underlined that the calculation of purely theoretical directcapture cross sections far from stability still contains a large error, even when using mostrecent nuclear-structure models. In the previously discussed case of Pb isotopes [5], ther-process path contains nuclei in or at the border of a region expected to be deformed,leading to higher level densities and thus favoring the compound nucleus mechanism.This is not true for neutron-rich isotopes in the Sn region, especially around the neu-tron magic number N = 82 where the level density becomes too low for the statisticalmodel. Therefore the neutron capture cross sections have to be calculated using inputfrom nuclear-structure models and will be subject to the quoted uncertainties, even whenthe different models yield similar values for other nuclear properties, such as masses.Similar problems may be encountered on the proton-rich side when predicting protoncapture cross sections close to the proton dripline.REFERENCES1. T. Rauscher, F.-K. Thielemann and K.-L. Kratz, Memorie della Societa` AstronomicaItaliana, in press.2. J. Dobaczewski et al., Phys. Rev. Lett. 72 (1994) 981.3. M.M. Sharma, G.A. Lalazissis, and P. Ring, Phys. Lett. B 317 (1993) 9.4. P. Mo¨ller and J.R. Nix, Nucl. Phys. A361 (1981) 117.5. T. Rauscher, R. Bieber, S. Lingner, and H. Oberhummer, AIP Conf. Proc. 327 (1995)183.6. K.H. Kim, M.H. Park and B.T. Kim, Phys. Rev. C 23 (1987) 363.7. A.M. Kobos, B.A. Brown, R. Lindsay, and G.R. Satchler, Nucl. Phys. A425 (1984)205.8. W. Balogh, R. Bieber, H. Oberhummer, T. Rauscher, K.-L. Kratz, P. Mohr, G. Staudt,and M.M. Sharma, Proc. Europ. Workshop on Heavy Element Nucleosynthesis, E.Somorjai and Z. Fu¨lo¨p (eds.), Inst. Nucl. Res. Hung. Acad. Sci., Debrecen 1994, p.67.9. S.F. Mughabghab, M. Divadeenam and N.E. Holden, Neutron Capture Cross Sections,Academic Press, New York, 1981.10. Data base CINDA, NNDC, Brookhaven National Laboratory, Upton, USA.11. F.-K. Thielemann, K.-L. Kratz, B. Pfeiffer, T. Rauscher, L. van Wormer, and M.Wiescher, Nucl. Phys. A570 (1995) 329c.

Memorie della Societa` Astronomica Italiana,

Neutron Capture Cross Sections,

Uncertainties In Direct Neutron Capture Calculations Due To Nuclear
  Structure Models

Uncertainties In Direct Neutron Capture Calculations Due To Nuclear Structure Models

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