arXiv subjects

N. K. Timofeyuk

Publications and source records attributed to N. K. Timofeyuk.

30 records · Page 2Linked to original sources

arXiv2014

$N$-boson spectrum from a Discrete Scale Invariance

We present the analysis of the $N$-boson spectrum computed using a soft two-body potential the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length $a$ close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground-state of the system with one less particle. It is governed by an unique universal function, $Δ(ξ)$, already known in the case of three bosons. In the three-particle system the angle $ξ$, determined by the ratio of the two- and three-body binding energies $E_3/E_2=\tan^2ξ$, characterizes the Discrete Scale Invariance of the system. Extending the definition of the angle to the $N$-body system as $E_N/E_2=\tan^2ξ$, we study the $N$-boson spectrum in terms of this variable. The analysis of the results, obtained for up to $N=16$ bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of $N$ is observed at fixed values of $a$. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length $a$ and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

cond-mat.quant-gas↗

arXiv2014

Efimov spectrum in bosonic systems with increasing number of particles

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length $a$ is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the $N$-body system by analysing the spectrum of $N$ identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the ground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. We discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to general $N$.

cond-mat.quant-gas↗

arXiv2014

Adiabatic model of $(d,p)$ reactions with explicitly energy-dependent non-local potentials

We have developed an approximate way of dealing with explicit energy-dependence of non-local nucleon optical potentials as used to predict the $(d,p)$ cross sections within the adiabatic theory. Within this approximation, the non-local optical potentials have to be evaluated at an energy shifted from half the incident deuteron energy by the $n-p$ kinetic energy averaged over the range of the $n-p$ interaction and then treated as an energy-independent non-local potential. Thus the evaluation of the distorting potential in the incident channel is reduced to a problem solved in our previous work in [{\it Phys. Rev. Lett. 110, 112501(2013) and Phys. Rev. C 87, 064610 (2013)}]. We have demonstrated how our new model works for the case of $^{16}$O$(d,p)^{17}$O, $^{36}$Ar($d,p)^{37}$Ar and $^{40}$Ca$(d,p)^{41}$Ca reactions and highlighted the need for a detailed understanding of energy-dependence of non-local potentials. We have also suggested a simple way of correcting the $d-A$ effective potentials for non-locality when the underlying energy-dependent non-local nucleon potentials are unknown but energy-dependent local phenomenological nucleon potentials are available.

nucl-th↗

arXiv2013

Rapid convergence of the Weinberg expansion of the deuteron stripping amplitude

Theories of $(d,p)$ reactions frequently use a formalism based on a transition amplitude that is dominated by the components of the total three-body scattering wave function where the spatial separation between the incoming neutron and proton is confined by the range of the $n$-$p$ interaction, $V_{np}$. By comparison with calculations based on the CDCC method we show that the $(d,p)$ transition amplitude is dominated by the first term of the expansion of the three-body wave function in a complete set of Weinberg states. We use the \nuc{132}{Sn}(d,p)\nuc{133} {Sn} reaction at 30 and 100 MeV as examples of contemporary interest. The generality of this observed dominance and its implications for future theoretical developments are discussed.

nucl-th↗

arXiv2009

A new insight into the observation of spectroscopic strength reduction in atomic nuclei: implication for the physical meaning of spectroscopic factors

Experimental studies of one nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a non-standard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon (NN) interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The method also reproduces the recently established relation between reduction of spectroscopic strength, observed in knockout reactions on other nuclei, and nucleon binding energies. The implication of the inhomogeneous equation method for the physical meaning of spectroscopic factors is discussed.

nucl-th↗

arXiv2008

Single-particle motion at large distances in 2N+core cluster systems near the drip line: a challenge for nuclear theory and experiment

There exists a class of nuclei that are obtained by adding one nucleon to a loosely-bound nucleon-core system, for example $^{12}$Be, $^9$C, $^{18}$Ne. For such nuclei, one-nucleon overlap integrals that represent single-particle motion can strongly differ from the standard ones due to the correlations between the two nucleons above the core. The possible non-standard overlap behaviour should be included in the interpretation of the experimental data derived from one nucleon removal reactions such as knockout, transfer and breakup, as well as the predictions of low-energy nucleon capture that leads to these nuclei. We investigate the non-standard behaviour within a three-body model and discuss the challenges associated with this problem.

nucl-th↗

arXiv2007

Long-range behaviour in hyperspherical formalism

It is shown that hyperspherical harmonics can be represented in a form typical of traditional microscopic cluster models. This allows those hyperharmonics that are responsible for long-range behaviour of valence nucleons in loosely-bound nuclei to be selected. The hyperspherical cluster model based on such hyperharmonics is tested for $^5$He using a simplified description of the $^4$He core and two versions of the Volkov potential which give $^5$He as either bound or unbound. The study has confirmed that it is possible to get a converged solution for binding energy, r.m.s. radius, overlap integral and asymptotic normalization coefficient with small number of basis functions for bound $^5$He. The values obtained of these quantities are very close to those calculated in a microscopic cluster model.

nucl-th↗

arXiv2005

Relation between widths of proton resonances and neutron asymptotic normalization coefficients in mirror states of light nuclei in a microscopic cluster model

It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003)) that the widths of narrow proton resonances are related to neutron Asymptotic Normalization Coefficients (ANCs) of their bound mirror analogs because of charge symmetry of nucleon-nucleon interactions. This relation is approximated by a simple analytical formula which involves proton resonance energies, neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. In the present paper, we perform microscopic-cluster model calculations for the ratio of proton widths to neutron ANCs squared in mirror states for several light nuclei. We compare them to predictions of the analytical formula and to estimates made within a single-particle potential model. A knowledge of this ratio can be used to predict unknown proton widths for very narrow low-lying resonances in the neutron-deficient region of the $sd$- and $pf$-shells, which is important for understanding the nucleosynthesis in the $rp$-process.

nucl-th↗

arXiv2005

Asymptotic normalization coefficients for mirror virtual nucleon decays in a microscopic cluster model

It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured with stable beams. In this work, we calculate one-nucleon ANCs for several light mirror pairs, using microscopic two-, three- and four-cluster models, and compare the ratio of mirror ANCs to the predictions of the simple analytic formula. We also investigate mirror symmetry between other characteristics of mirror one-nucleon overlap integrals, namely, spectroscopic factors and single-particle ANCs.

nucl-th↗

arXiv2003

A relation between proton and neutron asymptotic normalization coefficients for light mirror nuclei and its relevance to nuclear astrophysics

We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer reactions with stable beams.

nucl-th↗

arXiv2003

Do multineutrons exist?

Following recent work in which events which may correspond to a bound tetraneutron ($^4$n) were observed, it is pointed out that from the theoretical perspective the two-body nucleon-nucleon (NN) force cannot by itself bind four neutrons, even if it could bind a dineutron. Unrealistic modifications of the NN force or introduction of unreaslistic four-nucleon force would be needed in order to bind the tetraneutron. The existence of other multineutron systems is discussed.

nucl-th↗

arXiv2002

On the existence of a bound tetraneutron

Following recent work in which events which may correspond to a bound tetraneutron ($^4$n) were observed, it is pointed out that from the theoretical perspective the two-body nucleon-nucleon force cannot by itself bind four neutrons, even if it can bind a dineutron. A very strong phenomenological four-nucleon (4N) force is needed in order to bind the tetraneutron. Such a 4N force, if it existed, would bind $^4$He by about 100 MeV. Alternative experiments such as ($^8$He,$^4$n) are proposed to search for the tetraneutron.

nucl-th↗