Nuclear Deformability and Shell Structure

Marumori, Toshio; Suekane, Shingo; Yamamoto, Atsuko

doi:10.1143/ptp.16.320

Cited by 38 publications

(47 citation statements)

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“…It should be noted that the rigidity of 48 Ca is higher than one of the 40 Ca and reaches the maximal value for the nuclei with A < 50 -C( 48 Ca) ≈ 800 MeV. It should be noted that the ratio of rigidities of Ca isotopes extracted from the data on the mean-square deformations, does not agree with the corresponding results of the collective model calculations [7]. The latter, based on a specified scheme for quantum numbers and energy levels, have concluded that C( 40 Ca) > C( 48 Ca).…”

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confidence: 79%

The role of neutron pairs in nuclear collective properties

Goncharova

Tretyakova

Fedorov

2016

EPJ Web of Conferences

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Abstract. The role of surface neutrons in nuclear properties was examined by comparing rigidities of nuclear collective vibrations and charge radii of even-even nuclei. Correlations of peaks in rigidities and minimal values of r 0 = R ch · A −1/3 parameters were revealed.Eighty years of nuclear investigations have revealed a large variety in nuclear characteristics, their consistent theoretical interpretation is up to now only partly successful. For example, the theory of multipole giant resonances (MGR) observed experimentally in the cross sections of different reactions on even-even nuclei cannot explain in full extent a great variety of their forms and widths. E.g., in the region of middle-mass nuclei the giant E1 resonance has a complicated structure. It is a well-known phenomenon and many more or less successful attempts were made to describe the GR structure in magic and semimagic nuclei. However, as one can see from experimental data, sometimes addition of a couple of neutrons drastically changes the envelope of resonance peak.One may assume that one of the sources of diversity in the resonance shape is a variety of rigidities of nuclear surface. This characteristic of nuclei was discussed already at the dawn of nuclear physics when liquid drop model of nuclei was created [1,2].In the collective coordinate representation the Hamiltonian of the nuclear surface vibrations reads [1]where the momenta b λμ conjugate to collective coordinates a λμ which describe the deformation of nuclear surface. The coefficient B λ is the vibrational mass parameter. The rigidity C λ which determines the potential energy of nuclear deformation is connected with the nuclear surface tension. For the quadrupole surface vibrations (λ = 2) the connection of rigidity with the surface tension σ of a nucleus having the charge and radius Ze and R, respectively, has the formIt was already mentioned in [1] that the nuclear rigidity (deformability) may considerably vary from nucleus to a e-mail: n.g.goncharova@gmail.com nucleus and is strongly influenced by its shell structure. Nuclear rigidity as regards to quadrupole vibrations is connected with the energy of the first collective 2 + 1 state and the mean squared deformation of a nucleus βThe values of β were estimated and listed in [3] for all at that time available even-even nuclei. The estimations were based on the measured probabilities of quadrupole transitions to the ground states B(2). Certainly, the results are model dependent and the variations in the root-mean-square deformation estimations is less than 20%.In this work, we present the results of comparison of the calculated rigidities with the charge radii parameters for several isotopic chains of even-even nuclei. The data on the nuclear charge radii are taken from [4]. The dependence of nuclear charge radii on the neutron number is shown in [5].

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confidence: 79%

The role of neutron pairs in nuclear collective properties

Goncharova

Tretyakova

Fedorov

2016

EPJ Web of Conferences

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“…Due to the form factor (20), the forward peaks of angular distribution will slightly increase in comparison with the case of zero range nuclear force. The effect, however, may be negligible when the incident energy of neutron is below 5 Mev.…”

Section: Methods Of Approximation and Their Validitiesmentioning

confidence: 98%

Inelastic Scattering of Neutrons and Surface Direct Processes

1957

Prog. Theor. Phys.

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In the case of inelastic scattering of neutrons in which the residual nucleus is left in a definite low-lying excited state, the surface direct processes through single particle excitation and through ume sort of many particle excitations are formulated in a similar manner as in deuteron-stripping reaction. The distorted wave method is employed and its validity for the mentioned processes is discussed in some detail. The cross sections obtained are compared with that of another surface direct process accompanied by collective excitation and with that of the process through compound nucleus formation. It is shown that for intermediate and heavy nuclei (i) the collective excitation is much larger than the single particle excitation and (ii) the compound nucleus process is more important than the surface direct process in low energy region in which there are few open channels, while the latter is much larger than the former in higher energy region where many channels are open. § I. IntroductionIn recent experiments 1 > many evidences have been accumulated which clearly indicate the inadequacy of the concept of compound nucleus in explaining some of the nuclear reactions at moderate energies. One of the typical examples is the forward peaks of angular distribution appearing· in the case of inelastic scattering of particles in which the residual nucleus is left in a definite low-lying excited state. Such phenomena are evidently contradictory to the result of the statistical compound nucleus hypothesis.It, therefore, seems necessary to modify the concept of the compound nucleus, for instance, by removing some of the underlying assumptions, i. e., statistical assumption and continuum assumption, etc. Another possible and more realistic way of modification is to take into account such processes that take place without formation of the compound nucleus. These are called direct processes and may be divided into two classes : volume direct and surface direct processes. The former takes place inside of the nucleus, while the latter occurs at the diffuse layer at the nuclear boundary. The surface direct process may further be classified into various processes according to the mechanisms by which the target nucleus is excited. In the case of inelastic scattering of neutrons, Austern, Butler and McManus 2 > proposed the process by single particle excitation, whereas the direct process by collective excitation has been worked out by Hayakawa and Y oshida 3 >. As these mechanisms are of the extreme natures, there may be intermediate mechanisms of nuclear excitation, which may be called " group excitation ". a-particle excitation may be considered as one of the examples, in which a quasi a-particle in a nucleus is excited to its higher level to form residual nucleus. The mechanisms which work in actual nuclear reactions will be governed by the natures of target and residual nuclei.Downloaded from * Strictly speaking, the factor N depends on the detailed structure of the ground and excited states; under consideration. Its explicit ...

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“…:!l however, veff is dependent on the structure of the core through the collective eigen-&equencies, w1• This provides us with an explanation for the differences in the quadrupole moments of some isotopes. 6 > Secondly, the summation over n in (5 · 7) is usually carried out only for the main terms, and the applicability of configurational -mixing is restricted to the case of small perturbation. The same restriction holds in the collective model, in so far as the weak coupling approximation is employed.…”

Section: (6 · 3)mentioning

confidence: 99%

“…Thirdly, our method is different from the current collective model of A. Bohr.l7) In the latter case w 1 is determined on the basis of the hydrodynamical mode', whereas in our case w1 is obtained from the collective motion for a given rigidity which depends strongly upon the structure of the core. 6 where pP(x) is the density of protons and…”

Section: (6 · 3)mentioning

confidence: 99%

“…Table I. Calculated and ol::served valuEs of quadrupole moments in 10 The method of configurational mixing worked out by Arima and Horie 5 > and the collective model calculated by Marumori et al 6 l are found to have a common origin in accounting for nuclear quadrupole moments in the sense that the nuclear core is perturbed through fnteractions with extra-nucleons ; the interaction in the former method is ascribed to a nuclear force between a nucleon in the core and an extra-nucleon, while that in the latter ·is due to the deformation of the core induced by an extra-nucleon. The fluctuation in the values of quadrupole moments from nucleus to nucleus essentially depends upon how strongly the excited states of the core particles are admixed to their ground state.…”

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Relation between the Nuclear Collective Model and the Individual Particle Model with Configurational Mixing

Hayakawa

Marumori

1957

Prog. Theor. Phys.

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By using the method of the quantum mechanical description of collective motion, the relation between the collective model and the individual particle model with configurational mixing is discussed on the basis of the following postulates: (I) The wave function of the nucleus, as a system composed of actual nucleons, implies strong correlations, so that the Hartree approximation mak£s little sense. Consequently, the method of configurational mixing currently employed as well as the shell model may not be usable without altering the representation : (II) The strong correlation gives rise to collective motion, chiefly the sutface oscillation at low energies. The individual motion of nucleons which remains after subtraction of the collective motion is only weakly correlated, so that the shell model is a good approximatton to the individual motion.Leaving aside the essential problem of proving this statement, we reach the following conclusions concerning the relationship between the collective and the shell models of nuclei. i) The it).dividual particle model with configurational mixing does in fact hold in the case of small nuclear deformation, provided that the individual particle motion in the " collective represention " can be treated by means of the adiabatic approximation. ii) The elfective inter-particle force responsible for the configurational mixing consists of the following two parts, one arising from the exchange of surfons between an extra· particle and a particle in the .core and the other arising from a direct inter-particle interaction. iii) A1> far as the quadrupole moment is concerned, the collective model and the method of configurational mixing do not show any essential dilference. However, there exists an essential dilference in these two methods for the interpretation of the magnetic moments. *) Of course, the mixing of states of extra-particles may be caused. In this paper, however, we are rather interested in the relation between the method of configurational mixing and that of the collective model w we shall focts the discussion on the behaviour of the core in these two methods.

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Nuclear Deformability and Shell Structure

Cited by 38 publications

References 4 publications

The role of neutron pairs in nuclear collective properties

The role of neutron pairs in nuclear collective properties

Inelastic Scattering of Neutrons and Surface Direct Processes

Relation between the Nuclear Collective Model and the Individual Particle Model with Configurational Mixing

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