104 research outputs found

    Non-Scissors-Mode Behaviour of Isovector Magnetic Dipole Orbital Transitions Involving Isospin Transfer

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    We study the response of isovector orbital magnetic dipole (IOMD) transitions to the quadrupole-quadrupole (Q⋅QQ \cdot Q) interaction, to the isospin-conserving pairing interaction (ICP) and to combinations of both. We find qualitatively different behaviours for transitions in which the final isospin differs from the initial isospin versus cases where the two isospins are the same. For N=ZN=Z even-even nuclei with Jπ=0+,T=0J^{\pi}=0^+, T=0 ground states such as 8Be^8Be and 20Ne^{20}Ne, the summed T=0→T=1T=0 \to T=1 IOMD from the ground state to all the J=1,T=1J=1, T=1 states in the 0ℏω0 \hbar \omega space does not vanish when the Q⋅QQ \cdot Q interaction is turned off. The pairing interaction (ICP) alone leads to a finite transition rate. For nuclei with J=0+,T=1J=0^+, T=1 ground states such as 10Be^{10}Be and 22Ne^{22}Ne, the summed T=1→T=1T=1 \to T=1 IOMD doesdoes vanish when the Q⋅QQ \cdot Q interaction is turned off, as is expected in a good scissors-mode behaviour. However this is not the case for the corresponding sum of the T=1→T=2T=1 \to T=2 IOMD transitions. In 22Ne^{22}Ne (but not in 10Be^{10}Be) the sum of the T=1→T=2T=1 \to T=2 IOMD transitions is remarkably insensitive to the strengths of both the Q⋅QQ \cdot Q and the ICP interactions. In 22Ne^{22}Ne an energy weighted-sum is similarly insensitive. All our calculations were carried out in the 0ℏω0 \hbar \omega space.Comment: 19 pages (including 5 figures). submitted to Nucl. Phys.

    Effects of the Spin-Orbit and Tensor Interactions on the M1M1 and E2E2 Excitations in Light Nuclei

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    The effects of varying the spin-orbit and tensor components of a realistic interaction on M1M1 excitation rates and B(E2)â€ČsB(E2)'s are studied on nuclei in the 0p0p and 1s−0d1s-0d shells. Not only the total M1M1 but also the spin and orbital parts separately are studied. The single-particle energies are first calculated with the same interaction that is used between the valence nucleons. Later this stringent condition is relaxed somewhat and the 1s1s level is raised relative to 0d0d. For nuclei up to 28Si^{28}Si, much better results i.e stronger B(M1)B(M1) rates are obtained by increasing the strength of the spin-orbit interaction relative to the free value. This is probably also true for 32S^{32}S, but 36Ar^{36}Ar presents some difficulties. The effects of weakening the tensor interaction are also studied. On a more subtle level, the optimum spin-orbit interaction in the lower half of the s−ds-d shell, as far as M1M1 excitations are concerned, is substantially larger than the difference E(J=3/2+)1−E(J=5/2+)1=5.2 MeVE(J=3/2^+)_1-E(J=5/2^+)_1=5.2~MeV in 17O^{17}O. A larger spin-orbit splitting is also needed to destroy the triaxiality in 22Ne^{22}Ne. Also studied are how much M1M1 orbital and spin strength lies in an observable region and how much is buried in the grass at higher energies. It is noted that for many nuclei the sum B(M1)orbital+B(M1)spinB(M1)_{orbital}+B(M1)_{spin} is very close to B(M1)totalB(M1)_{total}, indicating that the summed cross terms are very small.Comment: 39 pages, revtex 3.

    Analytic expressions for the single particle energies with a quadrupole-quadrupole interaction and the relation to Elliott's SU(3) model

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    We present an analytical proof and a generalization of the Fayache-Sharon-Zamick relation between single particle energy splitting and the SU(3) limit in Elliott's model

    Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule

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    Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1+^+ excitations in even-even deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, the charge r.m.s. radius squared and Ï”\epsilon the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with available experimental data. The sum rule is derived using a simple ansatz for the intrinsic ground state wave function that predicts also high energy 1+^+ strength at 2ℏω\hbar \omega carrying 50\% of the total m1m_1 moment of the orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924

    Description of single and double analog states in the f7/2 shell: The Ti isotopes

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    The excitation energies of single analog states in even-odd Ti isotopes and double analog states in even-even Ti isotopes are microscopically described in a single j-shell formalism. A projection procedure for generalized BCS states has been used. As an alternative description a particle-core formalism is presented. The latter picture provides a two-parameter expression for excitation energies, which describes fairly well the data in four odd and three even isotopes of Ti.Comment: 14 pages,7 figures, 2 tables. To appear in Phys. Rev.

    Allowed Gamow-Teller Excitations from the Ground State of 14N

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    Motivated by the proposed experiment 14N(d,2He)14C^{14}N(d,{^2He})^{14}C, we study the final states which can be reached via the allowed Gamow-Teller mechanism. Much emphasis has been given in the past to the fact that the transition matrix element from the Jπ=1+T=0J^{\pi}=1^+ T=0 ground state of 14N^{14}N to the Jπ=0+T=1J^{\pi}=0^+ T=1 ground state of 14C^{14}C is very close to zero, despite the fact that all the quantum numbers are right for an allowed transition. We discuss this problem, but, in particular, focus on the excitations to final states with angular momenta 1+1^+ and 2+2^+. We note that the summed strength to the Jπ=2+T=1J^{\pi}=2^+ T=1 states, calculated with a wide variety of interactions, is significantly larger than that to the Jπ=1+T=1J^{\pi}=1^+ T=1 final states.Comment: Submitted to Phys. Rev.

    Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles

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    We present analytic proofs of the properties of four particle states in the g9/2 shell which have seniority v=4 and angular momentum I=4 or 6.We show in particular that the number of pairs with angular momentum I is equal to one for these states

    The Interference Term between the Spin and Orbital Contributions to M1 Transitions

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    We study the cross-correlation between the spin and orbital parts of magnetic dipole transitions M1 in both isoscalar and isovector channels. In particular, we closely examine certain cases where ∑B(M1)\sum B(M1) is very close to ∑B(M1)σ+∑B(M1)l\sum B(M1)_{\sigma} + \sum B(M1)_l, implying a cancellation of the summed interference terms. We gain some insight into this problem by considering special cases approaching the SU(3) limit, and by examining the behaviour of single-particle transitions at the beginning and towards the end of the s-d shell.Comment: 9 pages of latex file and no figure

    Shell-model test of the rotational-model relation between static quadrupole moments Q(2^+_1), B(E2)'s, and orbital M1 transitions

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    In this work, we examine critically the relation between orbital magnetic dipole (scissors mode) strength and quadrupole deformation properties. Assuming a simple K=0 ground state band in an even-even nucleus, the quantities Q(2^+_1) (i.e., the static quadrupole moment) and B(E2)_{0_1 \to 2_1} both are described by a single parameter--the intrinsic quadrupole moment Q_0. In the shell model, we can operationally define Q_0(Static) and Q_0(BE2) and see if they are the same. Following a brief excursion to the sd shell, we perform calculations in the fp shell. The nuclei we consider ({44,46,48}Ti and {48,50}Cr) are far from being perfect rotors, but we find that the calculated ratio Q_0(Static)/Q_0(BE2) is in many cases surprisingly close to one. We also discuss the collectivity of orbital magnetic dipole transitions. We find that the large orbital B(M1) strength in {44}Ti relative to {46}Ti and {48}Ti cannot be explained by simple deformation arguments.Comment: 12 pages, RevTeX4. Sections II (Quadrupole properties in the sd-shell) and V (Random interaction studies) added. Minor changes throughout the text and 48Cr added to present Table IV, as well as results for the lowest 100 state
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