Open problems in applying random-matrix theory to nuclear reactions

Weidenmueller, H.A.

doi:10.1088/0954-3899/41/9/094010

Cited by 9 publications

(10 citation statements)

References 34 publications

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“…The transport (stochastic) models are widely used to describe DIC [122][123][124][125][126][127][128][129]. The exchange of mass and charge and the transfer of energy and angular momentum from the relative motion to internal degrees of freedom can be successfully interpreted as a diffusion process.…”

Section: Theoretical Approaches To Deep-inelastic Collisionsmentioning

confidence: 99%

“…There are various transport models such as the randommatrix approximation [122,127], the model of one-body dissipation [128,129] and the linear-response model [126]. The main kinetic equation in these approaches is the master equation or Fokker-Planck equation for the distribution function of collective coordinates and conjugate momenta in the phase space of the collective degrees of freedom.…”

Section: Theoretical Approaches To Deep-inelastic Collisionsmentioning

confidence: 99%

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How to extend the chart of nuclides?

et al. 2020

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In the past 85 years the number of known nuclides increased by more than a factor of ten, resulting in 4000 presently known isotopes of 118 elements. This considerable progress we owe to the discovery of new reaction types along with the development of powerful accelerators and experimental techniques for separation and identification of reaction products. Model predictions indicate that still about 4000 further nuclides are waiting for their discovery. The vastest unexplored territory is located on the neutron-rich side in the upper half of the chart of nuclides and hides the answers to some of the most fundamental questions of nuclear physics like the limits of nuclear stability, element synthesis in the universe or stellar evolution. The access to these nuclei is presently limited by available beam intensities and/or the lack of appropriate methods for their production and identification. The latter concerns particularly new neutron-rich isotopes of transuranium and superheavy elements. To extend this area, the hope is presently based on multinucleon transfer reactions and on the application of fusion reactions with radioactive ion beams. But how promising are these approaches? Based on a survey of present-day knowledge, we will treat the questions where we currently are on our journey towards new territory on the chart of nuclides, how the chances are to gain new territory in the future and which challenges we will have to face.

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Section: Theoretical Approaches To Deep-inelastic Collisionsmentioning

confidence: 99%

Section: Theoretical Approaches To Deep-inelastic Collisionsmentioning

confidence: 99%

How to extend the chart of nuclides?

et al. 2020

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“…The focus in the present paper is on transition strengths which on one hand probe the structure of the eigenfunctions of a quantum manybody system and on the other are important ingredients in many applications (for example, beta decay transition strengths are essential for nucleosynthesis studies). Also, as emphasized in [2,8], there are many open questions in the random matrix theory for transition strengths in finite interacting quantum many-particle systems.…”

Section: Introductionmentioning

confidence: 99%

“…It is important to mention that in the present paper fluctuations in transition strengths are not considered and they will be addressed in a future publication. For some discussion on strength fluctuations see [2,8,9]. More importantly, using smoothed transition strengths statistical spectroscopy analysis of transition strengths (for example for particle transfer, electromagnetic transitions, beta decay and even double beta decay matrix elements) in nuclei and also in atoms is possible [18,19].…”

Section: Introductionmentioning

confidence: 99%

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Kota

Vyas

2015

Annals of Physics

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Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m fermions (or bosons) in N single particle states and interacting via k-body interactions, we have EGUE(k) [embedded GUE of k-body interactions) with GUE embedding and the embedding algebra is U(N). A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k) representation for a Hamiltonian that is k-body and an independent EGUE(t) representation for a transition operator that is t-body and employing the embedding U(N) algebra, finite-N formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for * Corresponding author. Phone: +91-79-26314464, Fax: +91-79-26314460Email addresses: vkbkota@prl.res.in (V.K.B. Kota), manan@fis.unam.mx (Manan Vyas) April 6, 2015 the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k 0 number of particles from a system of m spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French [Ann. Phys. (N.Y.) 95 (1975) 90]. Numerical results obtained using the exact formulas for two-body (k = 2) Hamiltonians (in some examples for k = 3 and 4) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed. Preprint submitted to Annals of Physics

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“…We observe much stronger fluctuations than for the total transmission, what is simply due to the fact that the latter implies an additional effective averaging over many scattering channels. As we will show now, this sensitive dependence on the energy is an unambiguous trait of (universal) Ericson fluctuations, that were hitherto only reported in the context of nuclear [24] and atomic physics [25], as well as in microwave experiments [26], and are also connected to universal conductance fluctuations in mesoscopic physics [27,28].…”

Section: Ericson Fluctuationsmentioning

confidence: 56%