arXiv subjects

Ikuko Hamamoto

Publications and source records attributed to Ikuko Hamamoto.

18 recordsLinked to original sources

arXiv2021

Deformed Halo of ^{29}_{9}F_{20}

Using a simple model based on the knowledge of spherical and deformed Woods-Saxon potentials, it is shown that the recent observation of halo phenomena in $^{29}$F can be interpreted as an evidence for the prolate deformation of the ground state of $^{29}$F. The prolate deformation is the result of the shell structure, which is unique in one-neutron resonant levels, in particular near degeneracy of the neutron 1$f_{7/2}$ and 2$p_{3/2}$ resonant levels, together with the strong preference of prolate shape by the proton number $Z$ = 9. On the other hand, in oxygen isotopes spherical shape is so much favored by the proton number $Z$ = 8 that the presence of possible neutron shell-structure may not make the system deformed. Thus, the strong preference of particular shape by the proton numbers 8 and 9, respectively, together with a considerable amount of the energy difference between the neutron $1d_{3/2}$ and $2s_{1/2}$ orbits in oxygen isotopes seems to play an important role in the phenomena of oxygen neutron drip line anomaly, as was suggested by H. Sakurai {\it et al.} in 1999.

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arXiv2019

Enhanced E1 transition between weakly-bound excited states in the nucleus 27Ne

Inspired by the recently-reported strong electric-dipole (E1) transition between the weakly-bound first and second excited states, 3/2- at 765 keV and 1/2+ at 885 keV, in the nucleus 27Ne, the E1 transition is estimated in a model by properly taking into account the effect of both deformation and weakly-bound neutrons. In addition to both the spin-parities, 1/2+ and 3/2-, and observed nearly degenerate energies of the two excited states, the observed order of magnitude of the E1 transition strength between the two states is very naturally explained in the case that these two excited states are prolately deformed, in terms of the transitions between the halo components of the wave functions of the weakly-bound odd-neutrons, s1/2 -> p3/2 and s1/2 -> p1/2, in addition to the large probability of the p3/2 component in the weakly-bound neutron [330 1/2] orbit. The large probability is the result of the shell-structure unique in weakly-bound or resonant neutrons.

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arXiv2019

Shape and shell-structure of lighter (N<90) neutron-rich nuclei based on phenomenological Woods-Saxon potential

By using a phenomenologically successful Woods-Saxon potential, I study the shape and shell structure of (A) neutron drip line nuclei with 10 \leq N \leq 60, (B) neutron-rich nuclei related to the r- process with 40 \leq N \leq 90, and (C) one-particle spectra in the potential provided by the nucleus 70Fe as a representative of so-called N=40 "island of inversion (IoI)" nuclei. First, the shell structure that is unique in very weakly-bound neutrons is systematically studied, and the approximate neutron number of odd-N nuclei at which spherical (or deformed) halos can be found is pinned down. Second, the difference of the shell structure in r-process nuclei from that in stable nuclei is examined. Third, the similarity and the difference between the shell structure of N=20 IoI nuclei and that of N=40 IoI nuclei are analyzed. As a result of it, it is concluded that in Fe and Cr isotopes the deformation called "N=40 IoI" continuing up to N=50 is unlikely.

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arXiv2017

Examining possible neutron-halo nuclei heaver than $^{37}$Mg

The even-Z odd-N neutron-halo nuclei, which are the possible lightest neutron-halo nuclei heavier than $^{37}$Mg, are explored by studying the shell-structure unique in weakly-bound neutrons for spherical or deformed shape. It is pointed out that due to the narrowed N=50 spherical energy-gap and a few resulting close-lying neutron one-particle levels, 1g$_{9/2}$, 3s$_{1/2}$, and 2d$_{5/2}$, for spherical shape, nuclei with some weakly-bound neutrons filling in those levels may be deformed and have a good chance to show deformed s-wave halo. Promising candidates are $^{71}_{24}$Cr$_{47}$, $^{73}_{24}$Cr$_{49}$, $^{75}_{24}$Cr$_{51}$ and $^{77}_{26}$Fe$_{51}$ in the case that those nuclei lie inside the neutron drip-line. An interesting possibility of the deformed p-wave or s-wave halo is suggested also for the nucleus $^{53}_{18}$Ar$_{35}$.

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arXiv2016

Shell-structure of one-particle resonances in deformed potentials

Shell structure of low-lying neutron resonant levels in axially-symmetric quadrupole-deformed potentials is discussed, which seems analogous to that of weakly-bound neutrons. As numerical examples, nuclei slightly outside the neutron-drip-line, $^{39}_{12}$Mg$_{27}$ and $^{21}_{6}$C$_{15}$, are studied. For the lowest resonance I obtain $I^π$ = $Ω^π$ = 5/2$^{-}$ for $^{39}$Mg which is likely to be prolately deformed, while $I^π$ = $Ω^π$ = 1/2$^{+}$ may be assigned to the nucleus $^{21}$C which may be oblately deformed. Consequently, $^{21}$C will not be observed as a recognizable resonant state, in agreement with the experimental information.

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arXiv2016

Interplay between one-particle and collective degrees of freedom in nuclei

Some developments of nuclear-structure physics uniquely related to Copenhagen School are sketched based on theoretical considerations versus experimental findings and one-particle versus collective aspects. Based on my personal overview I pick up the following topics; (1) Study of vibration in terms of particle-vibration coupling; (2) One-particle motion in deformed and rotating potentials, and yrast spectroscopy in high-spin physics; (3) Triaxial shape in nuclei: wobbling motion and chiral bands; (4) Nuclear structure of drip line nuclei: in particular, shell-structure (or magic numbers) change and spherical or deformed halo phenomena; (5) shell structure in oblate deformation.

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arXiv2014

Pigmy resonance in monopole response of neutron-rich Ni isotopes ?

The RPA monopole strength as well as the unperturbed particle-hole excitation strength is studied, in which the strength in the continuum is properly treated without discretizing unbound particle spectra. The model is the sef-consistent Hartree-Fock calculation and the RPA Green's function method with Skyrme interactions. Numerical examples are the Ni-isotopes, especially $^{68}_{28}$Ni$_{40}$, in which an experimental observation of low-lying socalled "pigmy resonance" with an appreciable amount of monopole strength at 12.9 $\pm$ 1.0 MeV was recently reported. In the present study it is concluded that sharp monopole peaks with the width of the order of 1 MeV can hardly be expected for $^{68}$Ni in that energy region. Instead, a broad shoulder of monopole strength consisting of neutron excitations to non-resonant one-particle states (called "threshold strength") with relatively low angular-momenta $(\ell, j)$ is obtained in the continuum energy region above the particle threshold, which is considerably lower than that of isoscalar giant monopole resonance. In the case of monopole excitations of $^{68}$Ni there are no unperturbed particle-hole states below 20 MeV, in which the particle expresses a neutron (or proton) resonant state. It is emphasized that in the theoretical estimate a proper treatment of the continuum is extremely important.

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arXiv2014

Oblate deformation of light neutron-rich even-even nuclei

Light neutron-rich even-even nuclei, of which the ground state is oblately deformed, are looked for, examining the Nilsson diagram based on realistic Woods-Saxon potentials. One-particle energies of the Nilsson diagram are calculated by solving the coupled differential equations obtained from the Schrödinger equation in coordinate space with the proper asymptotic behavior for $r \rightarrow \infty$ for both one-particle bound and resonant levels. The eigenphase formalism is used in the calculation of one-particle resonant energies. Large energy gaps on the oblate side of the Nilsson diagrams are found to be related to the magic numbers for the oblate deformation of the harmonic-oscillator potential where the frequency ratios ($ω_{\perp} : ω_{z}$) are simple rational numbers. In contrast, for the prolate deformation the magic numbers obtained from simple rational ratios of ($ω_{\perp} : ω_{z}$) of the harmonic-oscillator potential are hardly related to the particle numbers, at which large energy gaps appear in the Nilsson diagrams based on realistic Woods-Saxon potentials. The argument for an oblate shape of $^{42}_{14}$Si$_{28}$ is given. Among light nuclei the nucleus $^{20}_{6}$C$_{14}$ is found to be a good candidate for having the oblate ground state. In the region of the mass number $A \approx 70$ the oblate ground state may be found in the nuclei around $^{76}_{28}$Ni$_{48}$ in addition to $^{64}_{28}$Ni$_{36}$.

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arXiv2013

Possible Presence and Properties of Multi Chiral Pair-Bands in Odd-Odd Nuclei with the Same Intrinsic Configuration

Applying a relatively simple particle-rotor model to odd-odd nuclei, possible presence of multi chiral pair-bands is looked for, where chiral pair-bands are defined not only by near-degeneracy of the levels of two bands but also by almost the same expectation values of squared components of three angular-momenta that define chirality. In the angular-momentum region where two pairs of chiral pair-bands are obtained the possible interband M1/E2 decay from the second-lowest chiral pair-bands to the lowest chiral pair-bands is studied, with the intention of finding how to experimentally identify the multi chiral pair-bands. It is found that up till almost band-head the intraband M1/E2 decay within the second chiral pair-bands is preferred rather than the interband M1/E2 decay to the lowest chiral pair-bands, though the decay possibility depends on the ratio of actual decay energies. It is also found that chiral pair-bands in our model and definition are hardly obtained for $γ$ values outside the range $25^{\circ} < γ< 35^{\circ}$, although either a near-degeneracy or a constant energy-difference of several hundreds keV between the two levels for a given angular-momentum $I$ in "a pair bands" is sometimes obtained in some limited region of $I$. In the present model calculations the energy difference between chiral pair-bands is always one or two orders of magnitude smaller than a few hundreds keV, and no chiral pair-bands are obtained, which have an almost constant energy difference of the order of a few hundreds keV in a reasonable range of $I$.

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arXiv2012

Neutron shell structure and deformation in neutron-drip-line nuclei

Neutron shell-structure and the resulting possible deformation in the neighborhood of neutron-drip-line nuclei are systematically discussed, based on both bound and resonant neutron one-particle energies obtained from spherical and deformed Woods-Saxon potentials. Due to the unique behavior of weakly-bound and resonant neutron one-particle levels with smaller orbital angular-momenta $\ell$, a systematic change of the shell structure and thereby the change of neutron magic-numbers are pointed out, compared with those of stable nuclei expected from the conventional j-j shell-model. For spherical shape with the operator of the spin-orbit potential conventionally used, the $\ell_{j}$ levels belonging to a given oscillator major shell with parallel spin- and orbital-angular-momenta tend to gather together in the energetically lower half of the major shell, while those levels with anti-parallel spin- and orbital-angular-momenta gather in the upper half. The tendency leads to a unique shell structure and possible deformation when neutrons start to occupy the orbits in the lower half of the major shell. Among others, the neutron magic-number N=28 disappears and N=50 may disappear, while the magic number N=82 may presumably survive due to the large $\ell =5$ spin-orbit splitting for the $1h_{11/2}$ orbit. On the other hand, an appreciable amount of energy gap may appear at N=16 and 40 for spherical shape, while neutron-drip-line nuclei in the region of neutron number above N=20, 40 and 82, namely N $\approx$ 21-28, N $\approx$ 41-54, and N $\approx$ 83-90, may be quadrupole-deformed though the possible deformation depends also on the proton number of respective nuclei.

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arXiv2012

Shape Deformations in Atomic Nuclei

The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.

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arXiv2011

Selection Rule for Electromagnetic Transitions in Nuclear Chiral Geometry

In order to find the selection rules that can be applied to the electromagnetic transitions when the chiral geometry is achieved, a model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation. A quantum number obtained from the invariance of the Hamiltonian is given and the selection rule for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. Among the available candidates for chiral bands of odd-odd nuclei, in which the near degeneracy of two $ΔI = 1$ bands is observed, the measured electromagnetic properties of the two bands in $^{128}_{55}$Cs$_{73}$ and $^{126}_{55}$Cs$_{71}$ are consistent with the rules, while those of $^{134}_{59}$Pr$_{75}$ and $^{132}_{57}$La$_{75}$ are not.

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arXiv2010

Shell structure of weakly-bound and resonant neutrons

The systematic change of shell structure in both weakly bound and resonant neutron one-particle levels in nuclei towards the neutron drip line is exhibited, solving the coupled equations derived from the Schrödinger equation in coordinate space with the correct asymptotic behaviour of wave functions for $r \rightarrow \infty$. The change comes from the behaviour unique in the one-particle motion with low orbital angular momenta compared with that with high orbital angular momenta. The observed deformation of very neutron-rich nuclei with $N \simgeq 20$ in the island of inversion is a natural result of this changed shell structure, while a possible deformation of neutron-drip-line nuclei with $N \approx 51$, which are not yet observed, is suggested.

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arXiv2010

Change of shell structure and magnetic moments of odd-N deformed nuclei towards neutron drip line

Examples of the change of neutron shell-structure in both weakly-bound and resonant neutron one-particle levels in nuclei towards the neutron drip line are exhibited. It is shown that the shell-structure change due to the weak binding may lead to the deformation of those nuclei with the neutron numbers $N \approx$ 8, 20, 28 and 40, which are known to be magic numbers in stable nuclei. Nuclei in the "island of inversion" are most easily and in a simple manner understood in terms of deformation. As an example of spectroscopic properties other than single-particle energies, magnetic moments of some weakly-bound possibly deformed odd-N nuclei with neutron numbers close to those traditional magic numbers are given, which are calculated using the wave function of the last odd particle in deformed Woods-Saxon potentials.

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arXiv2009

Interpretation of Coulomb breakup of 31Ne in terms of deformation

The recent experimental data on Coulomb breakup of the nucleus $^{31}$Ne are interpreted in terms of deformation. The measured large one-neutron removal cross-section indicates that the ground state of $^{31}$Ne is either s- or p-halo. The data can be most easily interpreted as the spin of the ground state being 3/2$^-$ coming from either the Nilsson level [330 1/2] or [321 3/2] depending on the neutron separation energy $S_n$. However, the possibility of 1/2$^{+}$ coming from [200 1/2] is not excluded. It is suggested that if the large ambiguity in the measured value of $S_n$ of $^{31}$Ne, 0.29$\pm1.64$ MeV, can be reduced by an order of magnitude, say to be $\pm$100 keV, one may get a clear picture of the spin-parity of the halo ground state.

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arXiv2009

A further look at prolate dominance in nuclear deformation

The observed almost complete dominance of prolate over oblate deformations in the ground states of deformed even-even nuclei is related to the splitting of high $\ell$ "surface" orbits in the Nilsson diagram: on the oblate side the occurrence of numerous strongly avoided crossings which reduce the fanning out of the low $Λ$ orbits, while on the prolate side the same interactions increase the fanning out. It is further demonstrated that the prolate dominance is rather special for the restricted particle number of available nuclei and is not generic for finite systems with mean-field potentials resembling those in atomic nuclei.

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arXiv2008

One-particle properties of deformed N $\approx$ 28 odd-N nuclei with weakly-bound or resonant neutrons

Possible deformation of odd-N nuclei with N $\approx$ 28 towards the neutron drip line is investigated using the Nilsson diagram based on deformed Woods-Saxon potentials. Both weakly-bound and resonant one-particle levels are properly obtained by directly solving the Schrödinger equation in mesh of space coordinate with the correct boundary condition. If we use the same diffuseness of the potential as that of $β$-stable nuclei, the energy difference between the neutron 2p$_{3/2}$ and 1f$_{7/2}$ levels becomes very small or the N=28 energy gap almost disappears, as the binding energies of those levels approach zero. This suggests that the ground states of those neutron drip line nuclei are likely to be deformed. In particular, the spin-parity and the magnetic moment of the ground state of odd-N nuclei, $^{43}_{16}$S$_{27}$ and $^{45}_{16}$S$_{29}$, are examined. Moreover, it is suggested that in $^{39}_{12}$Mg$_{27}$ lying outside the drip line the lowest resonant state may have 5/2$^{-}$, if the N=28 energy gap almost vanishes.

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arXiv2007

Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons

Using Woods-Saxon potentials and the eigenphase formalism for one-particle resonances, one-particle bound and resonant levels for neutrons as a function of quadrupole deformation are presented, which are supposed to be useful for the interpretation of spectroscopic properties of some light neutron-rich nuclei with weakly-bound neutrons. Compared with Nilsson diagrams in text books which are constructed using modified oscillator potentials, we point out a systematic change of the shell structure in connection with both weakly-bound and resonant one-particle levels related to small orbital angular momenta $\ell$. Then, it is seen that weakly-bound neutrons in nuclei such as $^{15-19}$C and $^{33-37}$Mg may prefer to being deformed as a result of Jahn-Teller effect, due to the near degeneracy of the 1d$_{5/2}$-2s$_{1/2}$ levels and the 1f$_{7/2}$-2p$_{3/2}$ levels in the spherical potential, respectively. Furthermore, the absence of some one-particle resonant levels compared with the Nilsson diagrams in text books is illustrated.

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