Isobaric spin in heavy nuclei

Sliv, L.A.; Kharitonov, Yu.I.

doi:10.1016/0031-9163(65)90175-7

Cited by 46 publications

(23 citation statements)

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“…By using the perturbation theory [22] and the analytically solvable hydrodynamical model [23], the isospin mixing in atomic nuclei has been studied since the 1960s (see Ref. [24] for a review).…”

Section: Isospin Mixingmentioning

confidence: 99%

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Satuła¹,

Dobaczewski²,

Nazarewicz³

et al. 2011

Acta Phys. Pol. B

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Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N Z nuclei. By including simultaneous isospin and angular-momentum projection, we compute the isospin-breaking corrections to the 0 + → 0 + superallowed β-decay.

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Section: Isospin Mixingmentioning

confidence: 99%

Untitled

Satuła¹,

Dobaczewski²,

Nazarewicz³

et al. 2011

Acta Phys. Pol. B

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“…1-0.3)% for all stable nuclei with A > 40. Quantitative estimates performed by using the shell model [6][7][8] are approximately an order of magnitude larger than the estimate of Bohr and Mottelson. There are several factors that account for such a difference in the mentioned estimates.…”

Section: Introductionmentioning

confidence: 67%

“…The increase in the γ + parameter (in absolute value) with deformation is due to the effect of the reduced matrix element (E + ) on the value of the effective interaction potential in Eq. (6). As seen, the effective interaction depends on the multiplication of two commutators which contain the reduced matrix element (E ρ )(see Eq.…”

Section: Resultsmentioning

confidence: 99%

Deformation effects on isospin mixing and isobar analogue resonance for 74−80Kr isotopes

et al. 2014

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Abstract:Pyatov's method has been applied to investigate Fermi beta transitions in deformed 74−80 Kr isotopes. This self-consistent method, which was used to study the isobar analogue states in the spherical odd-odd nuclei, has to date not been applied for the isobar analogue states in deformed nuclei. The nucleon-nucleon residual interaction has been included so that the broken isospin symmetry in the mean field approximation has been restored and the strength parameter of the effective interaction has been taken out to be a free parameter. The energies and wave functions of the isobaric analogue excitations in 74−80 Rb isotopes have been obtained within the framework of the pnQRPA method. The probability of the isospin mixing in the ground states and the centroid energies of the isobar analogue resonance have been presented and the deformation effects on these quantities have been quantified. PACS

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“…On the other hand, if the right-hand side of (l\._ ·1) is used, we can derive a relation quite similar to (A· 4 For heavier nuclei the higher-order terms in the series (B · 4) are expected to become very small.…”

Section: '37mentioning

confidence: 90%

Theory of Hindered Gamow-Teller Matrix Elements

1967

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107The commutator method which was previously proposed for the purpose of calculating hindered matrix elements is applied to the Gamow.Teller beta matrix elements of heavier nuclei. It is shown that a number of empirical ft-values of the unfavored transitions can be well reproduced in terms of the conventional pairing model without invoking the phenomenological effective coupling constant. It is also shown that the !-forbidden transitions can be treated on the same footing as the unfavored ones. In such a treatment tensor forces play an important role. General forms of the effective single-body transition operators are derived on the basis of the commutator method, and qualitative discussions are given. § 1. Introduction Since the experimental discovery 1 l of the isobaric analogue states (IAS) in the (p, n) reactions of heavier nuclei, significant progress has been made 2 l, 3 l in understanding the role of isotopic spin for heavier nuclei. Several authors 3 l' 4 l discussed the extent of breakdown of the isospin symmetry for heavier nuclei and showed that the probability of admixed states with higher isospins is only about 3% for a very heavy nucleus. However, Lane and Soper 5 l asserted that even if the isospin is not a very good quantmn number, widths of the isobaric states can be very small ( < 100 ke V). The idea of "persistence of symmetry" which was thus born in the study of isobaric analogue states can also be applied to reexamining the beta decay matrix elements. 6 l' 7 l Actually the Gamow-Teller (GT) matrix element seems to be the best example of such a persistent symmetry, with which we shall be concerned in this paper.In general three stages of a broken symmetry can be defined; a) the exact, b) approximate and c) persistent symmetries. The first one does not correspond to any physical reality. The second one has a good example, namely the Fermi matrix elements J 1, as is clear from the arguments on the IAS. 7 J,SJ The ground or low-lying states of a heavier nucleus (N, Z) have an approximately good isospin T~Tz = (N-Z) /2, so that the Fermi transition from a ground to ground or a ground to low-lying states is expected to be severely hindered because of the isospin selection rule. However, such a consequence of symmetry requirement may persist in the case when the symmetry is significantly broken. An example of "persistent synunetry" is the Gamow-Teller transition.If the by guest on August 11, 2015 http://ptp.oxfordjournals.org/ Downloaded from 108 J. Fujita, Y. Futami and K. Ikeda supermultiplet symmetril is valid, the Gamow-Teller transitions among the states belonging to different supermultiplets are forbidden. However, even if the supermultiplet symmetry is significantly broken, the effect of the supermultiplet symmetry can survive according to terms. In other words, the supermultiplet model is not a good model for individual states of a heavy nucleus, but in considering a nucleus in reference to the neighboring one, we can recognize a clear trace of the symmetry requirement. (See Fig. 1.) a) b) ...

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Isobaric spin in heavy nuclei

Cited by 46 publications

References 1 publication

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Deformation effects on isospin mixing and isobar analogue resonance for 74−80Kr isotopes

Theory of Hindered Gamow-Teller Matrix Elements

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