Electro-excitation of the 1+ state at Ex = 3.486 MeV in 88Sr

doi:10.1016/0375-9474(84)90029-0

Nuclear Physics A

Volume 423, Issue 3, 23 July 1984, Pages 365-375

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Abstract

The differential cross section for excitation of the 1⁺ state at E_x = 3.486 MeV in ⁸⁸Sr by inelastic electron scattering has been measured for values of the momentum transfer f between 0.22 and 2.57 fm⁻¹. Both nuclear core polarization and Δ-hole polarization seem to be necessary to describe the observed reduction of the B(M1) value and data at low q and the behaviour of the cross section at intermediate values of q.

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Nucleon-pair approximation to the nuclear shell model
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Atomic nuclei are complex systems of nucleons–protons and neutrons. Nucleons interact with each other via an attractive and short-range force. This feature of the interaction leads to a pattern of dominantly monopole and quadrupole correlations between like particles (i.e., proton–proton and neutron–neutron correlations) in low-lying states of atomic nuclei. As a consequence, among dozens or even hundreds of possible types of nucleon pairs, very few nucleon pairs such as proton and neutron pairs with spin zero, two (in some cases spin four), and occasionally isoscalar spin-aligned proton–neutron pairs, play important roles in low-energy nuclear structure. The nucleon-pair approximation therefore provides us with an efficient truncation scheme of the full shell model configurations which are otherwise too large to handle for medium and heavy nuclei in foreseeable future. Furthermore, the nucleon-pair approximation leads to simple pictures in physics, as the dimension of nucleon-pair subspace is always small. The present paper aims at a sound review of its history, formulation, validity, applications, as well as its link to previous approaches, with the focus on the new developments in the last two decades. The applicability of the nucleon-pair approximation and numerical calculations of low-lying states for realistic atomic nuclei are demonstrated with examples. Applications of pair approximations to other problems are also discussed.
Nuclear response beyond mean field theory
1990, Nuclear Physics, Section A
An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in ⁴⁸Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to shortrange correlations as well as a possible stronger coupling to 2p2h states at low energy.
The broken pair model for nuclei and its recent applications
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The broken-pair model for nuclear structure is presented together with illustrative examples of its recent applications in various nuclear mass regions. The relationship with other models, in particular the shell model and the BCS model, is considered in some detail. The various ways in which the model has been presented in the literature are compared. The merits of several proposed extensions of the model are also discussed.
It is demonstrated that already the rather simple model with at most one broken pair can reproduce many properties of semic-magic nuclei. The rather complicated extension by breaking another pair is shown to be essential for the description of transitions between the excited states of the even semi-magic nuclei. The model, as presented here in a spherical shell model basis, is found to become less satisfactory for nuclei with several valence protons and neutrons. However, for such cases the broken-pair model provides considerable support for the use of the phenomenological boson models and may yield estimates for their parameters.
Consistent empirical description of magnetic moments and M1 transitions. Quenching of the diagonal and off-diagonal spin matrix elements
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The spin and tensor parts of an effective M1 operator for nuclei around ⁹⁰Zr and ²⁰⁸Pb are empirically determined by minimizing simultaneously the deviation of measured magnetic moments and M1 transitions from standard shell model calculations performed within lowest order shell-model spaces. The results are linked to a previous analysis of sd-shell nuclei and show approximately the mass dependence of the combined influence of high-lying many-particle-many-hole excitations admixed via the tensor force and of Δ-h admixtures.
Excitation of 1+ states in 88Sr by proton inelastic scattering
1985, Nuclear Physics, Section A
In a (p, p') study of ⁸⁸Sr at E_p = 201 MeV both a large resonance centered at 9.4 MeV excitation energy and the known 1⁺ state at 3.486 MeV are excited. Several discrete states are observed in the resonance. The cross section of the whole resonance is 27% of a simple particle-hole prediction. The strength of the low-lying 1⁺ state is only about 15% of that calculated from a wave function including core-polarization contributions, whereas (e, e') scattering finds about 50%.
Pairing correlation effects on the electron-scattering form factor of the 1+ state at 3.486 MeV in <inf>38</inf>88Sr<inf>50</inf>
1985, Physics Letters B

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^☆: Supported in part by the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (ZWO), and by the Deutsche Forschungs Gemeinschaft (DFG).

^∗: Present address: Philips Data Systems, Apeldoorn, The Netherlands.

^∗∗: Present address: Technische Universität München, D-8046 Garching, Germany.

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Nuclear Physics A

Abstract

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Nucleon-pair approximation to the nuclear shell model

Nuclear response beyond mean field theory

The broken pair model for nuclei and its recent applications

Consistent empirical description of magnetic moments and M1 transitions. Quenching of the diagonal and off-diagonal spin matrix elements

Excitation of 1<sup>+</sup> states in <sup>88</sup>Sr by proton inelastic scattering

Pairing correlation effects on the electron-scattering form factor of the 1<sup>+</sup> state at 3.486 MeV in <inf>38</inf><sup>88</sup>Sr<inf>50</inf>

Electro-excitation of the 1+ state at Ex = 3.486 MeV in 88Sr☆

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Electro-excitation of the 1⁺ state at E_x = 3.486 MeV in ⁸⁸Sr☆