An<i>ab initio</i>theory of double odd-even mass differences in nuclei

Saperstein, É. E.; Baldo, M.; Gnezdilov, N. V.; Lombardo, U.; Pankratov, S. S.

doi:10.1051/epjconf/20123805002

Cited by 7 publications

(19 citation statements)

References 20 publications

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“…The semi-microscopic model starts from the interaction V eff found in terms of a free NN potential (Argonne v 18 in our case), the gap equation being solved in the basis with the bare mass m * = m. Then the obtained EPI is supplemented with a phenomenological repulsive δ term proportional to a dimensionless parameter γ . The value of γ = 0.06 found in [14] to reproduce experimental gap values turned out to be also optimal for describing the DMD values in nonsuperfluid subsystems [26][27][28]. The phenomenological addendum supposedly embodies on average three different corrections to the simple BCS scheme [2,3]: the PC contribution, that from the effect of the effective mass m * =m, and the one due to the high-lying excitations.…”

Section: Discussionmentioning

confidence: 89%

“…Let us concentrate mainly on comparison of the column for (γ = 0.03) PC with the one corresponding to γ = 0.06 without PC corrections. The latter is representative of the original semimicroscopic model without PC corrections, with the optimal description of the pairing gap [14,15] and DMDs of nonsuperfluid components of semimagic nuclei [26][27][28] as well. The situation is essentially different for lighter nuclei, from 40 Ca to 56 Ni, and for heavier ones, beginning from 132 Sn.…”

Section: Calculation Resultsmentioning

confidence: 99%

“…Recently, the semi-microscopic model of the EPI V eff developed first for the pairing problem [11,14,15] was applied to the 034302-9 odd-even DMDs for nonsuperfluid subsystems of semimagic nuclei [26][27][28]. The DMD values are found by solving the inmedium Bethe-Salpeter equation with the same EPI V eff as that in the pairing gap equation.…”

Section: Discussionmentioning

confidence: 99%

“…In Refs. [26][27][28] this scheme of finding the DMD D +,− in nonsuperfluid systems within the semi-microscopic model was used for several chains of semimagic nuclei. The proton subsystem should be considered for isotopic chains with magic Z value, and the neutron one for isotonic chains where N is magic.…”

Section: B Double Mass Differences In Magic Nucleimentioning

confidence: 99%

“…The first such calculations with the use of the semi-microscopic model for the effective pairing interaction with the same value γ = 0.06 of the phenomenological parameter of the model, found previously in the pairing problem, were carried out recently for several semimagic chains [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Phonon effects on the double mass differences in magic nuclei

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Odd-even double mass differences (DMDs) of magic nuclei are found within an approach starting from the free NN interaction, accounting for particle-phonon coupling (PC) effects. We consider three PC effects: the phonon-induced effective interaction, the renormalization of the "ends" due to the pole PC contribution to the nucleon mass operator, and the change of the single-particle energies. The perturbation theory in g 2 L , where g L is the vertex of the creation of the L-multipole phonon, is used for PC calculations. PC corrections to single-particle energies are found with an approximate accounting for the tadpole diagram. Results for magic 40,48 Ca, 56,78 Ni, 100,132 Sn, and 208 Pb nuclei are presented. For the lighter part of this set of nuclei, from 40 Ca to 56 Ni, the cases divide approximately in half, between those where the PC corrections to DMD values are in good agreement with the data and the ones with the opposite result. In the major part of the cases of worsening description of DMD, a poor applicability of the perturbation theory for the induced interaction is the most probable reason of the phenomenon. For intermediate nuclei, 78 Ni and 100 Sn, there are no sufficiently accurate data on masses of nuclei necessary for finding DMD values. Finally, for heavier nuclei, 132 Sn and 208 Pb, PC corrections always result in better agreement with experiment.

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Section: Discussionmentioning

confidence: 89%

Section: Calculation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: B Double Mass Differences In Magic Nucleimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phonon effects on the double mass differences in magic nuclei

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Phonon–particle coupling effects in odd–even double mass differences of magic nuclei

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Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

et al. 2016

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A method is presented to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies (SPEs) in semi-magic nuclei. In such nuclei always there is a collective low-lying 2 + phonon, and a strong mixture of single-particle and particle-phonon states often occurs. As in magic nuclei, the so-called g 2 L approximation, where gL is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ PC (ε) to the initial mass operator Σ0. In addition to the usual pole diagram, the phonon "tadpole" diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ PC (ε) with respect to Σ0 is often invalid for finding the PC corrected SPEs. Instead, the Dyson equation with the mass operator Σ(ε)=Σ0+δΣ PC (ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented. 21.65.+f; 26.60.+c; 97.60.Jd Last decade, there was a revival of the interest within different self-consistent nuclear approaches to study the particle-phonon coupling (PC) effects in the singleparticle energies (SPEs) of magic nuclei. We cite here such studies within the relativistic mean-field theory [1], within the Skyrme-Hartree-Fock method [2,3,4] and on the basis of the self-consistent theory of finite Fermi systems (TFFS) [5]. The Fayans energy density functional (EDF) was used in the last case to find the self-consistent basis. In all the references cited above double-magic nuclei were considered. There are several reasons for such choice. First, these nuclei are nonsuperfluid which simplifies the theoretical analysis. Second, the so-called g 2 L approximation is, as a rule, valid in magic nuclei, g L being the vertex of the L-phonon creation. Moreover, the perturbation theory in terms of the PC correction to the mass operator ia also applicable, which makes evaluation of PC corrected SPEs rather simple. At last, there is a lot of experimental data on SPEs in these nuclei [6].In this work, we extend the field of this problem to semi-magic nuclei. Unfortunately, the experimental data on the SPEs in semi-magic nuclei are rather scarce. Indeed, the single-particle spectroscopic factor S of an excited state under consideration should be known. In addition, its value should be rather large, in order that one can interpret this state as a single-particle one. Extraction of the spectroscopic factors from the reaction 1) e-mail: Sapershtein EE@nrcki.ru data is a complicated theoretical problem, therefore the list of known spectroscopic factors is rather limited. However, the PC corrections to the SPEs are necessary not only by themselves, they are also usually important ingredients of the procedure of finding PC corrections to other nuclear characteristics, e.g., magnetic moments and M 1 transitions in odd nuclei [7,8,9]. PC corrections to the double odd-even mass differences found in the approach starting from the free N N potential [10,11] is another example where the PC corrections to SPEs are of primary importance.A semi-mag...

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Anab initiotheory of double odd-even mass differences in nuclei

Cited by 7 publications

References 20 publications

Phonon effects on the double mass differences in magic nuclei

Phonon effects on the double mass differences in magic nuclei

Phonon–particle coupling effects in odd–even double mass differences of magic nuclei

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

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