# Dr Natalia Timofeyuk

### Research

### Research interests

Nuclear Reaction Theory

Hyperspherical Harmonics formalism

### Research projects

### Research collaborations

Universite Libre de Bruxelles

University of Pisa

Moscow State University

### My publications

### Publications

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,

$\Delta(\xi)$, already known in the case of three bosons. In the three-particle

system the angle $\xi$, determined by the ratio of the two- and three-body

binding energies $E_3/E_2=\tan^2\xi$, characterizes the Discrete Scale

Invariance of the system. Extending the definition of the angle to the $N$-body

system as $E_N/E_2=\tan^2\xi$, 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.

coefficients for light mirror nuclei and its relevance to nuclear

astrophysics, Phys.Rev.Lett. 91 pp. 232501-232501

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.

non-local potentials, Physical Review C: Nuclear Physics

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.

in a microscopic cluster model, Phys.Rev.C 71 pp. 064305-064305

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.

normalization coefficients in mirror states of light nuclei in a microscopic

cluster model, Phys.Rev. C 72 pp. 064324-064324

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.

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.

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.

of one-nucleon overlap functions for 0p-shell nuclei calculated in the source term approach using shell model

wave functions. The tabulated data includes both new results and updates on previously published values. They

are compared with recent results obtained in ab initio calculations, and with experimental data, where available.

The reduction of spectroscopic factors with respect to traditional shell model values as well as its neutron-proton

asymmetry is also discussed

15

F

,

16

Ne

, and

19

Na

were investigated by measuring the angular correlations between protons and the respective heavy-ion fragments stemming from the precursor decays in flight. The parent nuclei of interest were produced in nuclear reactions of one-neutron removal from

17

Ne

and

20

Mg

projectiles at energies of 410?450

A

MeV. The trajectories of the respective decay products,

14

O

+

p

+

p and

18

Ne

+

p

+

p, were measured by applying a tracking technique with microstrip detectors. These data were used to reconstruct the angular correlations of the fragments, which provided information on energies and widths of the parent states. In addition for reproducing properties of known states, evidence for hitherto unknown excited states in

15

F

and

16

Ne

was found. This tracking technique has an advantage in studies of exotic nuclei beyond the proton drip line measuring the resonance energies and widths with a high precision although by using low-intensity beams and very thick targets.

A

(

d

,

p

)

B

reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon (

3

N

) force. The purpose of this paper is to study the contribution of the

3

N

force of the simplest possible form to the

A

(

d

,

p

)

B

reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between

A

and

B

. The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the

3

N

interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact

3

N

force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the

3

N

contribution is noticeable, especially at high deuteron incident energies. No

3

N

effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the

3

N

contribution to the

(

d

,

p

)

cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model.

can be very sensitive to the n-p interactions used in the adiabatic treatment of deuteron breakup

with nonlocal nucleon-target optical potentials. To understand to what extent this sensitivity could

originate in the inaccuracy of the adiabatic approximation we have developed a leading-order local-equivalent continuum-discretized coupled-channel model that accounts for non-adiabatic effects in

the presence of nonlocality of nucleon optical potentials. We have applied our model to the astro-physically relevant reaction

^{26m}Al(d, p)

^{27}Al using two different n-p potentials associated with the

lowest and the highest n-p kinetic energy in the short-range region of their interaction, respectively.

Our calculations reveal a significant reduction of the sensitivity to the high n-p momenta thus confirming that it is mostly associated with theoretical uncertainties of the adiabatic approximation

itself. The non-adiabatic effects in the presence of nonlocality were found to be stronger than those

in the case of the local optical potentials. These results argue for extending the analysis of the (d, p)

reactions, measured for spectroscopic studies, beyond the adiabatic approximation.

*Z*=50 (for

*N*Ã 82) and

*Z*= 82 (for

*N*Ã 126). The level of forbiddenness of the n=1

*v*1g

_{9/2} À0g

_{7/2}transition has been investigated from the ² decay of the ground state of

^{207}Hg into the single-proton-hole nucleus

^{207}Tl in an experiment at the ISOLDE Decay Station. From statistical observational limits on possible ³-ray transitions depopulating the À0g

^{-1}

_{7/2}state in

^{207}Tl, an upper limit of 3.9 x 10

^{-3}% was obtained for the probability of this decay, corresponding to log

*ft*Ã 8.8 within a 95% confidence limit. This is the most stringent test of the n=0 selection rule to date.

*d, p*) reactions has been known for a long time. It arises when the nonlocal two-body deuteron-target and/or proton-target problem is approximated by a local one, manifesting itself in a reduction of the scattering channel wave functions in the nuclear interior. However, the (

*d, p*) reaction mechanism requires explicit accounting for three-body dynamics involving the target and the neutron and proton in the deuteron. Treating nonlocality of the nucleon-target interactions within a three-body context requires significant effort and demands going beyond the widely-used adiabatic approximation, which can be done using a continuum-discretized coupled-channel (CDCC) method. However, the inclusion of nonlocal interactions into the CDCC description of (

*d, p*) reactions has not been developed yet. Here, we point out that, similarly to the two-body nonlocal case, nonlocality in a three-body channel can be accounted for by introducing the Perey factors. We explain this procedure and present the first CDCC calculations to our knowledge including the Perey effect.

^{40}Ca(

*d, p)*

^{41}Ca reaction where experimental data both on elastic scattering in entrance and exit channels and on nucleon transfer are available.

*d,p*) reactions, Physical Review C 99 (6) 064612 pp. 064612-1 American Physical Society

*A(d,p)B*reactions relies on solving a three-body

*A+n+p*Schrödinger equation with pairwise

*A?n, A?p*and

*n?p*interactions. However, it was shown in Phys. Rev. C 89, 024605 (2014) that projection of the many-body

*A+2*wave function into the three-body

*A+n+p*channel results in a complicated three-body operator that cannot be reduced to a sum of pairwise potentials. It contains explicit contributions from terms that include interactions between the neutron and proton via excitation of the target

*A*. Such terms are normally neglected. We estimate the first-order contribution of these induced three-body terms and show that applying the adiabatic approximation to solving the

*A+n+p*model results in a simple modification of the two-body nucleon optical potentials. We illustrate the role of these terms for the case of

^{40}Ca(

*d,p*)

^{41}Ca transfer reactions at incident deuteron energies of 11.8, 20, and 56 MeV, using several parametrizations of nonlocal optical potentials.

to study the structure of nuclei. Today these experiments are often carried out in inverse kinematics in state-of-the-art radioactive beams facilities around the world, extending the boundaries of

our knowledge of the nuclear chart. The nuclear structure information obtained from these experiments relies entirely on transfer reaction theory. We review the theory of (d; p) and (p; d) reactions

starting from early formulations and ending with the most recent developments. In particular,

we describe the recent progress made in the understanding of the three-body dynamics associated

with the deuteron breakup degrees of freedom, including effects of nonlocality, and discuss the

role of many-body degrees of freedom within the three-body context. We also review advances

in structure model calculations of one-nucleon overlap functions - an important structure input

to (d; p) and (p; d) reaction calculations. We emphasize the physics missing in widely-used standard approaches available to experimentalists and review ideas and efforts aimed at including this

physics, formulating the crucial tasks for further development of deuteron stripping and pickup

reaction theory