High-energy scissors mode

Nojarov, R.; Faessler, Amand; Dingfelder, M.

doi:10.1103/physrevc.51.2449

Cited by 25 publications

(36 citation statements)

References 50 publications

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“…The expression for the magnetic cross section applies to both convection and spin current contributions. Although the above estimates (14) are in agreement with previous results [19,7], the q-dependence in (14) is qualitatively different.…”

Section: Pwba Analysis For Small Momentum Transfersupporting

confidence: 90%

“…The scattering angle is however fixed in modern experiments [4,2] and the form factor is studied by measurements for different incident energies. One has to apply in this case the estimates (14). They are more general since they are valid also for a fixed incident energy.…”

Section: Pwba Analysis For Small Momentum Transfermentioning

confidence: 99%

“…The choice of the parameters of the model hamiltonian is explained in more detail elsewhere [14]. In contrast to many other microscopic calculations, energies of single-particle levels are not shifted but taken exactly as provided by the deformed Woods-Saxon potential.…”

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confidence: 99%

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Angular and energy dependence of (e, e′) cross sections for orbital 1+ excitations

1996

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The main features of the (e, e ′ ) cross sections of low-lying orbital excitations with K π = 1 + in heavy deformed nuclei are studied in RPA on the example of 156 Gd.The dependence of the DWBA E2 and M1 cross sections on the scattering angle 0 • < θ < 180 • and incident electron energy E i < 210 MeV is analyzed in PWBA.The cross section is larger for M1 than for E2 transitions at any angle if E i < 30MeV. The longitudinal (Coulomb) C2 excitation dominates the E2 response for 5 • < θ < 170 • . Only transverse M1 and E2 excitations compete for θ > 175 • and the former one is dominant for q < 1.2 fm −1 . The M1 response is almost purely orbital up to q = 1.4 fm −1 even in backward scattering. Qualitative PWBA estimates based on the q-dependence of the form factors alone are not able to predict some important features of the (e, e ′ ) cross sections stemming from the strong magnetic and orbital character of the studied 1 + excitations. The expectation for M1 over E2 dominance in backward scattering should not be extended to higher momentum transfers and incident energies.The backward inelastic electron scattering has established itself in the last 30 years as one of the main tools for the experimental study of nuclear magnetic excitations. The attention was focused in the past mainly on spherical nuclei, as it can be seen, e.g., from the review articles [1,2]. The detailed study of low-lying magnetic dipole (M1) excitations in heavy deformed nuclei started with (e, e ′ ) experiments at the linear accelerator in Darmstadt [3], reviewed recently in [4]. Most of the data were collected at a backward scattering angle θ = 165 • , where one expects a strong damping of electric excitations. This can be understood from qualitative considerations [5, 6] in the plane wave Born approximation (PWBA). The (e, e ′ ) cross section can be decomposed in this case into longitudinal (Coulomb) and transverse (electric and magnetic) terms, multiplied by corresponding kinematic factors. The longitudinal kinematic factor V ℓ (θ) vanishes for θ = 180 • and only transverse multipoles are excited in backward scattering [5]. Among those with the same multipolarity, the magnetic excitation is dominant over the electric transverse one [6]. This qualitative estimate is obtained in the long-wave limit qR ≪ 1, or small momentum transfer q in comparison with the radius R of the target nucleus. Magnetic dominance was found at backward angle also in [1] by assuming a purely spin-flip transition. The more realistic distorted wave Born approximation (DWBA) [7] leads to important corrections especially in heavy nuclei with a strong Coulomb field (a large charge number Z). But this approach is not suitable for simple qualitative predictions, since the longitudinal and transverse electric contributions to the (e, e ′ ) cross section interfere with each other in DWBA. Moreover, their separation would be meaningless when the longitudinal and transverse electric contributions are related in the DWBA formalism [8, 9] through the continuity equation.In contras...

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Section: Pwba Analysis For Small Momentum Transfersupporting

confidence: 90%

Section: Pwba Analysis For Small Momentum Transfermentioning

confidence: 99%

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Angular and energy dependence of (e, e′) cross sections for orbital 1+ excitations

1996

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“…We solve the QRPA equations of motion for intrinsic excitations with K = 1+ using a model Hamiltonian [29] H = H0+ HFF+ Hss, …”

Section: Transition Densities In the Qrpamentioning

confidence: 99%

Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei

1995

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Important E2 contributions to the (e, e ) cross sections of low-lying orbital Ml excitations are found in heavy deformed nuclei, arising from the small energy separation between the two excitations with I K= 2+1 and 1+1,respectively. They are studied microscopically in QRPA using DWBA. The accompanying E2 response is negligible at small momentum transfer q but contributes substantially to the cross sections measured at t/= 165' for 0.6(q,«(0.9 fm ' (40~E;~70 MeV) and leads to a very good agreement with experiment. The electric response is of longitudinal C2 type for (9~175 but becomes almost purely transverse E2 for larger backward angles. The transverse E2 response remains comparable with the M1 response for q, «) 1.2 fm ' (E;~100 MeV) and even dominant for E;)200 MeV. This happens even at large backward angles 0~175', where the M1 dominance is limited to the lower q region. PACS number(s): 25.30.Dh, 21.60.Jz, 27.70.+q I. MOTIVATION Inelastic electron scattering at a backward angle 0=180' was used by Peterson and co-workers [1,2] more than 30 years ago to study nuclear magnetic dipole (Ml) excitations at the linear accelerator in Stanford. The predominance of M 1 excitations in backward scattering is expected from qualitative considerations [2] of the (e,e ') cross section in the plane wave Born approximation (PWBA). The cross section can be decomposed in this case into longitudinal (Coulomb) and transverse (electric and magnetic) terms, multiplied by corresponding kinematical factors. The electric field of the incoming electron can have both longitudinal and transverse components, while its magnetic field is purely transverse. If the electron rest mass and the nuclear excitation energy can be neglected in comparison with the incident electron energy, which is often the case with low-lying excitations, the longitudinal kinematical factor vanishes for 0=180' and only transverse multipoles are excited by the inelastic scattering [3]. The (e, e ') cross section can be related further to the transition probability for photoabsorption through approximate considerations within the "virtual photon" method. One arrives in this way at the rough qualitative estimate [2] for dominant magnetic over electric transverse excitations (both of the same multipolarity). This property is due to the momentum transfer during electron scattering. It stands in contrast with the corresponding relationship for radiative excitation, where no momentum is transferred and the EL excitation is one order of magnitude stronger than the ML excitation (L stands for multipolarity). Electronic address: roland. noj arov uni-tuebingen. dẽ Electronic address: amand. faessler uni-tuebingen. dẽ Electronic address: michael. ding felder uni-tuebingen. de dominance at a backward angle can be drawn by assuming a purely spin-fiip transition [4]. The transverse electric field of the incoming electron is negligibly small in this particular case if the excitation energy E is small in comparison with the transferred momentum q, i.e. , E &&qfi, c. The same result...

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“…The microscopic origin of such a term is not understood. Recently, there has been an analysis by Nojarov, Faessler and Dingfelder [8] and by Nojarov [9] of the isovector part of the optical potential and they feel that it should be weaker than in previous analyses.…”

Section: Closing Remarksmentioning

confidence: 99%

The isospin-dependent quadrupole-quadrupole interaction used in shell model calculations – the effects of including ΔN = 2 excitations and a two-body spin-orbit interaction term

Fayache

Sharon

Zamick

et al. 2000

EPJ A

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The effect of the "B" term in the interaction −χQ(1) · Q(2)[1 + Bτ (1) · τ (2)] was previously considered in the 0p shell (small space). It is now studied in a larger space which additionally includes ∆N = 2 excitations. When B is made sufficiently negative we still obtain for 10 Be, even in the larger space, an unphysical collapse of some of the low-lying states so that their energies are less than the energy of the conventional J = 0 + ground state. This effect, however, occurs for values of B considerably more negative than was the case in the smaller space. It is shown that the inclusion of an additional two-body spin-orbit interaction term prevents this unrealistic collapse in both the large and small spaces.

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High-energy scissors mode

Cited by 25 publications

References 50 publications

Angular and energy dependence of (e, e′) cross sections for orbital 1+ excitations

Angular and energy dependence of (e, e′) cross sections for orbital 1+ excitations

Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei

The isospin-dependent quadrupole-quadrupole interaction used in shell model calculations – the effects of including ΔN = 2 excitations and a two-body spin-orbit interaction term

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