We report on the first measurement of the elemental fragmentation cross sections (EFCSs) of <math><mmultiscripts><mrow><mi>Si</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>29</mn><mo>−</mo><mn>33</mn></mrow></mmultiscripts></math> on a carbon target at ∼230 MeV/nucleon. The experimental data covering charge changes of ΔZ = 1-4 are reproduced well by the isospin-dependent quantum molecular dynamics (IQMD) coupled with the evaporation GEMINI (IQMD+GEMINI) model. We further explore the mechanisms underlying the single-proton removal reaction in this model framework. We conclude that the cross sections from direct proton knockout exhibit an overall weak dependence on the mass number of Si projectiles. The proton evaporation induced after the projectile excitation significantly affects the cross sections for neutron-deficient Si isotopes, while neutron evaporation plays a crucial role in the reactions of neutron-rich Si isotopes. It is presented that the relative magnitude of one-proton and one-neutron separation energies is an essential factor that influences evaporation processes. Therefore, proton evaporation should be incorporated into the reaction model in addition to the direct proton knockout in analyses of Gade-Tostevin systematic for single-proton removal reactions.

China

Guang-Shuai Li

Bao-Hua Sun

Jun Su

Japan

Isao Tanihata

Satoru Terashima

Germany

Jian-Wei Zhao

Er-Xi Xiao

Ji-Chao Zhang

Liu-Chun He

Ge Guo

Wei-Ping Lin

Wen-Jian Lin

Chuan-Ye Liu

Chen-Gui Lu

Bo Mei

Dan-Yang Pang

Ye-Lei Sun

Zhi-Yu Sun

Meng Wang

Feng Wang

Jing Wang

Shi-Tao Wang

Xiu-Lin Wei

Xiao-Dong Xu

Jun-Yao Xu

Li-Hua Zhu

Yong Zheng

Mei-Xue Zhang

Xue-Heng Zhang

Single-proton removal reaction in the IQMD+GEMINI model benchmarked by elemental fragmentation cross sections of Si on carbon at ∼230 MeV/nucleon

The spin-orbit splitting between neutron 1p orbitals at $^{33}$Si has been deduced using the single-neutron-adding (d,p) reaction in inverse kinematics with a beam of $^{32}$Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1p-shell orbitals is systematically studied using the present and existing data in the isotonic chains of <math><mi>N</mi><mo>=</mo><mn>17</mn></math>, 19, and 21. In each case, a smooth decrease in the separation of the <math><mn>1</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math>-<math><mn>1</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> orbitals is seen as the respective p-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region.

United States

J. Chen

B.P. Kay

C.R. Hoffman

T.L. Tang

I.A. Tolstukhin

D. Bazin

R.S. Lubna

Spain

Y. Ayyad

S. Beceiro-Novo

Australia

B.J. Coombes

United Kingdom

CERN

S.J. Freeman

L.P. Gaffney

R. Garg

H. Jayatissa

A.N. Kuchera

P. MacGregor

A.J. Mitchell

W. Mittig

B. Monteagudo

A. Munoz-Ramos

C. Müller-Gatermann

Italy

F. Recchia

N. Rijal

C. Santamaria

M.Z. Serikow

D.K. Sharp

J. Smith

J.K. Stecenko

G.L. Wilson

A.H. Wuosmaa

C.X. Yuan

J.C. Zamora

Y.N. Zhang

Evolution of the nuclear spin-orbit splitting explored via the Si( , ) Si reaction using SOLARIS

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around <math><mi>N</mi><mo>=</mo><mn>28</mn></math>, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of $^{40}$Mg, $^{42}$Si, and $^{44}$S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that $^{40}$Mg and $^{42}$Si exhibit large deformations. After that, the erosion of the <math><mi>N</mi><mo>=</mo><mn>28</mn></math> shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in <math><mi>N</mi><mo>=</mo><mn>28</mn></math> even-even isotones ranging from $^{40}$Mg to $^{48}$Ca. Finally, the shell evolution of <math><mi>N</mi><mo>=</mo><mn>28</mn></math> in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of $^{40}$Mg and $^{42}$Si.

Q. Yuan

J.G. Li

H.H. Li

Calculations for Well Deformed Nuclei: Mg and Si

Scattering amplitudes in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.

Mexico

L. Bossinger

J. Drummond

R. Glew

Adjacency for scattering amplitudes from the Gröbner fan

Quasi-elastic (QEL) scattering measurements have been performed using a $^{28}$Si projectile off a $^{90}$Zr target at energies around the Coulomb barrier. A Bayesian analysis within the framework of coupled channels (CC) calculations is performed in a large parameter space of quadrupole and hexadecapole deformations (<math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub></math>) of $^{28}$Si. Our results unambiguously show that $^{28}$Si is an oblate shaped nucleus with <math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math>=-<math><mn>0.38</mn><mo>±</mo><mn>0.01</mn></math> which is in excellent agreement with results from electromagnetic probes. The sign and magnitude of quadrupole deformation along with a precise value of hexadecapole deformation (<math><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub></math>=+<math><mn>0.03</mn><mo>±</mo><mn>0.01</mn></math>) of $^{28}$Si have been determined for the first time using QEL scattering. A remarkable agreement is obtained between the experimental and calculated <math><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub></math> values of $^{28}$Si based on Skyrme-Hartree-Fock method. The present results demonstrate the strong sensitivity of the quasi-elastic scattering to the sign and magnitude to the ground state deformation parameters, thus affirming its suitability to be used for rare exotic nuclei using low intensity RIBs.

India

Y.K. Gupta

V.B. Katariya

G.K. Prajapati

K. Hagino

D. Patel

V. Ranga

U. Garg

L.S. Danu

A. Pal

B.N. Joshi

S. Dubey

V.V. Desai

S. Panwar

N. Kumar

S. Mukhopadhyay

Pawan Singh

N. Sirswal

R. Sariyal

I. Mazumdar

B.V. John

Precise determination of quadrupole and hexadecapole deformation parameters of the -shell Nucleus, Si

New magic numbers have been discovered in the neutron-rich region of the nuclear chart. However, there has been a lack of research on proton-rich nuclei. $^{22}$O, the mirror nucleus of $^{22}$Si, is a double-magic nucleus bearing a high <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math>. Whether $^{22}$Si exhibits double-magic characters is an intriguing topic. To investigate this matter, we utilized ab initio valence space in-medium similarity renormalization group for $^{22}$Si/$^{22}$O, and their nearby nuclei. Our ab initio calculations provide good descriptions for the double magicity of $^{22}$O, as well as the shell evolution of <math><mi>N</mi><mo>=</mo><mn>14</mn></math> and <math><mi>Z</mi><mo>=</mo><mn>14</mn></math> through <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math>. The computed <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math> indicate that the closure of <math><mi>Z</mi><mo>=</mo><mn>14</mn></math> sub-shell in proton-rich nuclei is weaker than the <math><mi>N</mi><mo>=</mo><mn>14</mn></math> sub-shell closure in their mirror nuclei. Particularly, the calculated <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math> of $^{22}$Si is 800 keV lower than the one of $^{22}$O. To further explore the magicity of $^{22}$Si, the mirror energy difference (MED) of $^{26}$Si/$^{26}$Mg, $^{24}$Si/$^{24}$Ne, as well as $^{22}$Si/$^{22}$O are calculated. The results demonstrate that the calculated MEDs agree well with available experimental data, and the <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math> values of $^{22,24,26}$Si are all lower than their respective mirror nuclei due to the Thomas-Ehrman shift with large <math><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> occupation. Moreover, our calculation provides that the many-body configurations of the low-lying state of $^{22}$Si/$^{22}$O are nearly identical despite the fact that the states bearing large MED. In conclusion, our ab initio results suggest that $^{22}$Si is a double magic nucleus, similar to its mirror nucleus $^{22}$O, albeit with a lower <math><mi>E</mi><mo>(</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math>.

S. Zhang

Y.M. Xing

W. Zuo

Double-magicity of proton drip-line nucleus Si with Calculation

We present an analysis on the heavy flavor hadron decay electrons with charm and beauty contributions decomposed via a data driven method in p+p and Pb+Pb collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt></math> = 5.02 TeV at LHC. The transverse momentum <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> spectra, nuclear modification factor <math><msub><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow></msub></math> and azimuthal anisotropic flow <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> distributions of electrons from charm and beauty decays are obtained. We find that the electron <math><msub><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow></msub></math> from charm (<math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow><mrow><mi>c</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math>) and beauty (<math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math>) decays are suppressed at <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>&gt;</mo><mn>2.0</mn></math> GeV/c in Pb+Pb collisions, which indicates that charm and beauty interact with and lose their energy in the hot-dense medium. A less suppression of <math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math> than <math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow><mrow><mi>c</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math> at <math><mn>2.0</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>&lt;</mo><mn>8.0</mn></math> GeV/c is observed, which is consistent with the mass-dependent partonic energy loss scenario. A non-zero electron <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> from beauty decays (<math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math>) is observed and in good agreement with ALICE measurement. At low <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> from 1.0 to 3.0 GeV/c, a discrepancy between RHIC and LHC results is observed with an 85% confidence level, which might be a possible hint of an energy-dependent behavior of beauty quarks reacting with the medium created in heavy-ion collisions. At <math><mn>3.0</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>&lt;</mo><mn>7.0</mn></math> GeV/c, <math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math> deviates from a number-of-constituent-quark (NCQ) scaling hypothesis, which favors that beauty quark is unlikely thermalized in heavy-ion collisions at LHC energy.

Dongsheng Li

Fan Si

Yidan Zhao

Pengyu Zhou

Yifei Zhang

Xiujun Li

Chengxi Yang

Charm and beauty isolation from heavy flavor decay electrons in p+p and Pb+Pb collisions at = 5.02 TeV at LHC

We report on a new measurement of the beam-normal single spin asymmetry <math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math> in the elastic scattering of 570 MeV transversely polarized electrons off $^{28}$Si and $^{90}$Zr at <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.04</mn><msup><mrow><mtext> GeV</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. The studied kinematics allow for a comprehensive comparison with former results on $^{12}$C. No significant mass dependence of the beam-normal single spin asymmetry is observed in the mass regime from $^{12}$C to $^{90}$Zr.

A. Esser

M. Thiel

P. Achenbach

K. Aulenbacher

S. Aulenbacher

S. Baunack

Croatia

D. Bosnar

S. Caiazza

M. Christmann

M. Dehn

M.O. Distler

L. Doria

P. Eckert

M. Gorchtein

P. Gülker

P. Herrmann

M. Hoek

S. Kegel

P. Klag

H.J. Kreidel

M. Littich

S. Lunkenheimer

F.E. Maas

M. Makek

H. Merkel

Slovenia

M. Mihovilovič

J. Müller

U. Müller

J. Pochodzalla

B.S. Schlimme

R. Spreckels

V. Tioukine

C. Sfienti

Beam-normal single spin asymmetry in elastic electron scattering off Si and Zr

The reduction of the neutron spin-orbit (SO) splitting <math><mn>2</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>−</mo><mn>2</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> between the $^{41}$Ca and $^{35}$Si isotones is a unique feature throughout the chart of nuclides, as the SO splitting usually increases with decreasing A. The way it is reduced, either gradually between $^{41}$Ca and $^{35}$Si or abruptly between $^{37}$S and $^{35}$Si, as well as the origin of its reduction, whether from the weak binding energy of the p states or from the sudden depletion in the central proton density moving to $^{35}$Si, are subject of debate. The results reported here using the self-consistent Covariant Energy Density Functional calculations with the DD-ME2 parametrization rather point to an abrupt, local decrease in $^{35}$Si, and to the large dominance of the central density depletion effect. It is concluded that weak binding, central density depletion as well as correlations must be taken into account to fully evaluate the amplitude and causes of this SO splitting reduction. To broaden the scope of the present work, discussions also include the recent experimental results of proton and neutron SO splittings around $^{132}$Sn and $^{56}$Ni.

France

O. Sorlin

F. de Oliveira Santos

J.P. Ebran

Reduced spin-orbit splitting in Si: Weak binding or density-depletion effect?

We present a study of charm and beauty isolation based on a data-driven method with recent measurements on heavy flavor hadrons and their decay electrons in Au+Au collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt></math> = 200 GeV at RHIC. The individual electron <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> spectra, <math><msub><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow></msub></math> and <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> distributions from charmed and beauty hadron decays are obtained. We find that the electron <math><msub><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow></msub></math> from beauty hadron decays (<math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>AA</mi></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math>) is suppressed in minimum bias Au+Au collisions but less suppressed compared with that from charmed hadron decays at <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> &gt; 3.5 GeV/c, which indicates that beauty quark interacts with the hot-dense medium with depositing its energy and is consistent with the mass-dependent energy loss scenario. For the first time, the non-zero electron <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math> from beauty hadron decays (<math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math>) at <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> &gt; 3.0 GeV/c is observed and shows smaller elliptic flow compared with that from charmed hadron decays at <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> &lt; 4.0 GeV/c. At 2.5 GeV/c &lt; <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> &lt; 4.5 GeV/c, <math><msubsup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>b</mi><mo>→</mo><mi>e</mi></mrow></msubsup></math> is smaller than a number-of-constituent-quark (NCQ) scaling hypothesis. This suggests that beauty quark is unlikely thermalized and too heavy to be moved in a partonic collectivity in heavy-ion collisions at the RHIC energy.

Xiao-Long Chen

Long Zhou

Yi-Fei Zhang

Sheng-Hui Zhang

Xin-Yue Ju

Xiu-Jun Li

Xin Dong

Nu Xu

Charm and beauty isolation from heavy flavor decay electrons in Au+Au collisions at = 200 GeV at RHIC