Variational approach to anharmonic collective motion

Abstract. We propose a new method to extract the collective masses and momenta associated with a given set of collective coordinates, along a dynamical microscopic mean-field evolution. We apply our method to the symmetric fission of 258 Fm nucleus, and analyze the dynamical evolution of the system in the collective space. We compare, between the dynamical and the adiabatic paths, the force acting on the quadrupole degree of freedom, which is closely related to the relative distance between fragments. It is shown that dynamical effects beyond the adiabatic limit are important for formation and scission of the neck between emitted fragments.

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“…Similar expressions for momentum [23] and for mass (see for instance [24][25][26]) are also found in literature.…”

Section: Mass and Momentum Associated With Collective Coordinatesupporting

confidence: 54%

Collective aspects of microscopic mean-field evolution along the fission path

Tanimura

Lacroix

Scamps

2016

EPJ Web of Conferences

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“…In fact, anharmonicities influence electromagnetic DGDR cross sections in several ways: (a) the energy shifts of the DGDR states from the harmonic values can affect in an important way the electromagnetic cross section, in keeping with the exponential dependence of these quantities with the Q value of the process [22], (b) anharmonicities lead to changes in the E1 transition matrix elements to preserve the energy weighted sum rule (EWSR) [23] which eventually reinforce these effects, (c) anharmonicities which are a consequence of the mixing of states with different number of phonons give rise to many paths, other than the (harmonic) two-step one, to excite the DGDR in electromagnetic processes. While all these questions inspired much theoretical work [24][25][26][27][28][29][30][31][32][33][34], no clear picture has emerged of the DGDR anharmonicity question, let alone an explanation of the "Coulomb excitation anomaly." In particular, no consensus exists concerning the mass-number dependence of the energy shifts from the harmonic values.…”

Section: (Received 15 May 2000)mentioning

confidence: 99%

Anharmonic Properties of the Double Giant Dipole Resonance

Ponomarev

et al. 2000

Phys. Rev. Lett.

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A systematic microscopic study of the anharmonic properties of the double giant dipole resonance (DGDR) has been carried out, for the first time, for nuclei with mass number A spanning the whole mass table. It is concluded that the corrections of the energy centroid of the Jpi = 0(+) and 2(+) components of the DGDR from its harmonic limit are negative, have a value of the order of a few hundred keV, and follow an A-1 dependence.

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“…The anharmonic behavior of the giant resonances as a possibility to explain the increase of the Coulomb excitation cross sections has been studied by several authors 23,24 (see also ref. 25 , and references therein). It was found that the effect is indeed negligible and it could be estimated 25 as ∆ (2) E < E GDR /(50A) ∼ A −4/3 MeV.…”

Section: Anharmonicitiesmentioning

confidence: 99%

Relativistic Heavy Ion Excitation of Giant Resonances

Bertulani

2003

Electromagnetic Probes of Fundamental Physics

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Giant resonances and giant resonances built on other giant resonances in nuclei are observed with very large cross sections in relativistic heavy ion collisions. A theoretical effort is underway to understand the reaction mechanism which leads to this process, as well as a better understanding of the microscopic properties of multiphonon states, e.g., their strength, energy centroids, widths and anharmonicities.1 Giant Resonances Single giant resonancesGiant resonances in nuclei were first observed in 1937 by Bothe and Gentner 1 who obtained an unexpectedly large absorption of 17.6 MeV photons (from the 7 Li(p,γ) reaction) in some targets. These observations were later confirmed by Baldwin and Klaiber (1947) with photons from a betatron. In 1948, Goldhaber and Teller 2 interpreted these resonances (called isovector giant dipole resonances (IVGDP)) with a hydrodynamical model in which rigid proton and neutron fluids vibrate against each other, the restoring force resulting from the surface energy. Steinwendel and Jensen 3 later developed the model, considering compressible neutron and proton fluids vibrating in opposite phase in a common fixed sphere, the restoring force resulting from the volume symmetry energy. The standard microscopic basis for the description of giant resonances is the random phase approximation (RPA) in which giant resonances appear as coherent superpositions of one-particle one-hole (1p1h) excitations in closed shell nuclei or two quasiparticle excitations in open shell nuclei (for a review of these techniques, see, for example, ref. 4 ). The isoscalar quadrupole resonances were discovered in inelastic electron scattering by Pitthan and Walcher (1971) and in proton scattering by Lewis and Bertrand (1972). Giant monopole resonances were found later and their properties are closely related to the compression modulus of nuclear matter. Following these, other resonances of higher multipolarities and giant magnetic resonances were investigated. Typical probes for giant resonance studies are (a) γ's and electrons for the excitation of IVGDR, (b) α-particles and electrons for the excitation of isoscalar giant monopole resonance (ISGMR) and giant quadrupole resonance (ISGQR), and (c) (p, n), or ( 3 He, t), for Gamow-Teller resonances, respectively. Multiphonon resonancesInelastic scattering studies with heavy ion beams have opened new possibilities in the field (for a review of the recent developments, see ref. 5 ). A striking feature was observed when either the beam energy was increased, or heavier projectiles were used, or both 6 . This is displayed in figure a

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Variational approach to anharmonic collective motion

Cited by 38 publications

References 32 publications

Collective aspects of microscopic mean-field evolution along the fission path

Collective aspects of microscopic mean-field evolution along the fission path

Anharmonic Properties of the Double Giant Dipole Resonance

Relativistic Heavy Ion Excitation of Giant Resonances

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