We have studied the nuclear structure properties like binding energy, charge radius, quadrupole deformation parameter for various isotopes of Al from the valley of stability to drip line region using the well known relativistic mean field formalism (RMF) with NL3 parameter set. We have compared our results with experimental data and found reasonable agreement. Further, we have taken spherical and deformed RMF densities to estimate the reaction dynamics of $^{23-28}$Al isotopes as projectiles and $^{12}$C as target by conjunction in Glauber model. The estimated results are also compared with the experimental data. The analysis of angular elastic differential and one proton removal cross sections are also studied with Glauber model many body system to investigate the structural feature of $^{23}$Al. The evidence of enhanced total reaction cross section, higher value of rms radius, narrow longitudinal momentum distribution and small proton separation energy of $^{23}$Al support its proton halo structure.
The experimentally predicted existence of a proton halo in $^8$B is confirmed by dynamical microscopic multiconfiguration cluster model calculations. The thickness of the proton halo in $^8$B is 0.5 $fm$ while in $^8$Li a 0.4 $fm$ thick neutron halo has been found. It is shown that the huge quadrupole moment of $^8$B partly comes from the very distortable $^7$Be core.
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scattering states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
Charged pion photoproduction is proposed as a new method to study halo nuclei. In particular, it is demonstrated that the reaction 17O(gamma,pi^-)17F(1/2+, 0.495 MeV) is well-suited to investigate the well-known proton halo in 17F which is not amenable to radioactive beam experiments. The cross sections are shown to be very sensitive to the halo structure of the loosely bound proton.
The nuclide $^{17}$Ne is studied theoretically in a three-body $^{15}$O+$p$+$p$ model. We demonstrate that the experimental condition for existence of a proton halo in $^{17}$Ne can be reasonably quantified in terms of $s/d$ configuration mixing. We discuss experimental evidences for a proton halo in $^{17}$Ne. We define which kind of experimental data could elucidate this issue.
We analyze the effects of finite-range corrections in halo effective field theory for S-wave proton halo nuclei. We calculate the charge radius to next-to-leading order and the astrophysical S-factor for low-energy proton capture to fifth order in the low-energy expansion. As an application, we confront our results with experimental data for the S-factor for proton capture on Oxygen-16 into the excited $1/2^+$ state of Fluorine-17. Our low-energy theory is characterized by a systematic low-energy expansion, which can be used to quantify an energy-dependent model error to be utilized in data fi…
To explain the experimental facts that the fusion cross sections of proton-halo nucleus on heavy target nucleus is not enhanced as expected, the shielding supposition has been proposed. Namely, the proton-halo nucleus is polarized with the valence proton being shielded by the core. In this paper, within the frame of the Improved Quantum Molecular Dynamics model, the fusion reactions by $^{17}$F on $^{208}$Pb around Coulomb barrier have been simulated. The existence of shielding effect is verified by microscopic dynamics analysis and its influence on the effective interaction potential is also …
Theoretical investigation of two-proton halo-nucleus 17Ne has revealed that the valence protons are more likely to be positioned in the d-state than the s-state. In this study, this finding is clarified by calculation of the binding energy, it is found that the theoretical values for the d-state are closer to the experimental values, in contrast with those obtained for the s-state. The three-body model and MATLAB software are utilised to obtain theoretical values for the three-body-model 17Ne binding energy and matter radius. 17Ne has halo properties of a weakly bound valence proton, a binding…
We investigate the intense X-ray laser-induced proton emission from halo nuclei within the framework of a nonperturbative quantum $S$-matrix approach. We have analytically deduced the angular differential as well as the total multi-photon rates of the proton emissions. For a linearly polarized X-ray laser field, we find that the angular distributions of proton emission sensitively depend on the laser frequency and show an interesting petal structure with increasing the laser frequency as well as the number of absorbed photons. Meanwhile, we find the Coulomb repulsion potential between the prot…
The Glauber theory has been used to investigate the reaction cross section of proton-rich nucleus $^{23}$Al. A core plus a proton structure is assumed for $^{23}$Al. HO-type density distribution is used for the core while the density distribution for the valence proton is calculated by solving the eigenvalue problem of Woods-Saxon potential. The transparency function in an analytical expression is obtained adopting multi-Gaussian expansion for the density distribution. Coulomb correction and finite-range interaction are introduced. This modified Glauber model is apt for halo nuclei. A dominate…
The interaction cross sections for $^A Na + ^{12}C$ reaction are calculated using Glauber model. The continuum Hartree-Bogoliubov theory has been generalized to treat the odd particle system and take the continuum into account. The theory reproduces the experimental result quite well. The matter distributions from the proton drip line to the neutron drip line in Na isotopes have been systematically studied and presented. The relation between the shell effects and the halos has been examined. The tail of the matter distribution shows a strong dependence on the shell structure. The neutron N=28 …
A comparison between full few-body Faddeev/Alt-Grassberger-Sandhas (Faddeev/AGS) and continuum-discretized coupled channels (CDCC) calculations is made for the resonant and nonresonant breakup of $^{11}$Be on proton target at 63.7 MeV/u incident energy. A simplified two-body model is used for $^{11}$Be which involves an inert $^{10}$Be(0$^+$) core and a valence neutron. The sensitivity of the calculated observables to the nucleon-nucleon potential dynamical input is analysed. We show that with the present NN and N-core dynamics the results remain a puzzle for the few-body problem of scattering…
E2 properties of A=6--10 nuclei, including those of nuclei far from stability, are studied by a $(0+2)\hbarω$ shell-model calculation which includes E2 core-polarization effects explicitly. The quadrupole moments and the E2 transition strengths in A=6--10 nuclei are described quite well by the present calculation. This result indicates that the relatively large value of the quadrupole moment of $^8$B can be understood without introducing the proton-halo in $^8$B. An interesting effect of the $2\hbarω$ core-polarization is found for effective charges used in the $0\hbarω$ shell model; although …
We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energies $E_b$ and two neutron separation energies $S_{2n}$ very well. The predicted neutron drip line nuclei are $^{28}$O, $^{72}$Ca, $^{98}$Ni, $^{136}$Zr, $^{176}$Sn, and $^{266}$Pb, respe…
Nuclei at both the neutron- and proton-drip lines are studied. In the cluster-core model, the halo-structure of all the observed and proposed cases of neutron- or proton-halos is investigated in terms of simple potential energy surfaces calculated as the sum of binding energies, Coulomb repulsion, nuclear proximity attraction and the centrifugal potential for all the possible cluster+core configurations of a nucleus. The clusters of neutrons and protons are taken to be unbound, with additional Coulomb energy added for proton-clusters. The model predictions agree with the available experimental…
This work addresses the question of precisely what features of few body models of halo nuclei are probed by elastic scattering on protons at high centre-of-mass energies. Our treatment is based on a multiple scattering expansion of the proton-projectile transition amplitude in a form which is well adapted to the weakly bound cluster picture of halo nuclei. In the specific case of $^{11}$Li scattering from protons at 800 MeV/u we show that because core recoil effects are significant, scattering crosssections can not, in general, be deduced from knowledge of the total matter density alone. We ad…
We perform coupled-cluster calculations of the energies and lifetimes of single-particle states around the doubly magic nucleus 16O based on chiral nucleon-nucleon interactions at next-to-next- to-next-to-leading order. To incorporate effects from the scattering continuum, we solve the coupled- cluster equations with a Gamow-Hartree-Fock basis. Our calculations for the 1/2+ proton-halo state in 17F and the 1/2+ state in 17O agree well with experiment, while the calculated spin-orbit splitting between d5/2 and d3/2 states is too small due to the lack of three-nucleon forces. We find that contin…
We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order are applied to study the excited 1/2+ state of Fluorine-17, and we give results for the charge radius and the astrophysical S-factor.
In this short note we use a simple model to describe the dynamical effects of break-up processes in the subbarrier fusion involving weakly bound nuclei. We model two similar cases involving either a neutron or a proton halo nucleus, both schematically coupled to the break-up channels. We find that the decrease of the coulomb barrier in the proton break-up channel leads, ceteris paribus, to a larger enhancement of the subbarier fusion probabilities with respect to the neutron-halo case.
The ratio method has been developed to improve the study of one-neutron halo nuclei through reactions. By taking the ratio of angular distributions for two processes, viz. breakup and elastic scattering, this new observable is nearly independent of the reaction mechanism and hence much more sensitive to the projectile structure than the cross sections for each single process. We study the extension of the ratio method to proton-rich nuclei and also explore the optimum experimental conditions for measuring this new observable. We compare accurate dynamical calculations of reactions for proton-r…
In this paper we show how effective parameters such as effective binding energies can be defined for a proton in the combined nuclear-Coulomb potential, including also the target potential, in the case in which the proton is bound in a nucleus which is partner of a nuclear reaction. Using such effective parameters the proton behaves similarly to a neutron. In this way some unexpected results obtained from dynamical calculations for reactions initiated by very weakly bound proton halo nuclei can be interpreted. Namely the fact that stripping dominates the nuclear breakup cross section which in …
I investigate the elastic electron scattering off nuclei far from the stability line. The effects of the neutron and proton skins and halos on the differential cross sections are explored. Examples are given for the charge distribution in Sn isotopes and its relation to the neutron skin. The neutron halo in $^{11}$Li and the proton halo in $^{8}$B are also investigated. Particular interest is paid to the inverse scattering problem and its dependence on the experimental precision. These studies are of particular interest for the upcoming electron ion colliders at the GSI and RIKEN facilities.
Two-proton radioactivity with 2p halo is reported theoretically in light mass nuclei A $=$ 18-34. We predict $^{19}$Mg, $^{22}$Si, $^{26}$S, $^{30}$Ar and $^{34}$Ca as promising candidates of ground state 2p-radioactivity with S$_{2p}$ $<$ 0 and S$_{p}$ $>$ 0. Observation of extended tail of spatial charge density distribution, larger charge radius and study of proton single particle states, Fermi energy and the wave functions indicate 2p halo like structure which supports direct 2p emission. The Coulomb and centrifugal barriers in experimentally identified 2p unbound $^{22}$Si show a quasi-bo…
With the relativistic Coulomb wave function boundary condition, the energies, widths and wave functions of the single proton resonant orbitals for $^{17}$Ne are studied by the analytical continuation of the coupling constant (ACCC) approach within the framework of the relativistic mean field (RMF) theory. Pairing correlations and contributions from the single-particle resonant orbitals in the continuum are taken into consideration by the resonant Bardeen-Cooper-Schrieffer (BCS) approach, in which constant pairing strength is used. It can be seen that the fully self-consistent calculations with…
The exotic structures in the 2s_{1/2} states of five pairs of mirror nuclei ^{17}O-^{17}F, ^{26}Na-^{26}P, ^{27}Mg-^{27}P, ^{28}Al-^{28}P and ^{29}Si-^{29}P are investigated with the relativistic mean-field (RMF) theory and the single-particle model (SPM) to explore the role of the Coulomb effects on the proton halo formation. The present RMF calculations show that the exotic structure of the valence proton is more obvious than that of the valence neutron of its mirror nucleus, the difference of exotic size between each mirror nuclei becomes smaller with the increase of mass number A of the mi…
With the binding energies and configurations determined experimentally, the root-mean-square radii are calculated for a number of single-particle states by numerically solving the Sch{ö}rdinger equations. By studying the relations between the radii and separation energies, the new scaling laws and necessary conditions for neutron halos and proton halos are established, respectively. Especially the existence region of true proton halos is pointed out. It is found that the effects of short-distance behaviours of valence nucleons at the edges of interaction potentials can not be disregarded. More…
Nuclei with large neutron-to-proton ratios have neutron skins, which manifest themselves in an excess of neutrons at distances greater than the radius of the proton distribution. In addition, some drip-line nuclei develop very extended halo structures. The neutron halo is a threshold effect; it appears when the valence neutrons occupy weakly bound orbits. In this study, nuclear skins and halos are analyzed within the self-consistent Skyrme-Hartree-Fock-Bogoliubov and relativistic Hartree-Bogoliubov theories for spherical shapes. It is demonstrated that skins, halos, and surface thickness can b…
The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $β$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body model for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e.\ a lower bound $6 \times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 \times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausib…
Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\text{Be}(\text{d},\,\text{p}){}^{11}\text{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In contrast, the deuteron and the beryllium-11 halo nucleus are generated dynamically from contact interactions using experimental and ab initio input. The reaction amplitude is constructed up to next-to-lea…
Neutron and proton densities in the nuclear periphery are investigated within (p,n) charge-exchange isobar transitions. For this purpose we have developed parameter-free optical potentials with a detailed treatment of the in-medium $t_τ$ part of the effective interaction. Non local coupled-channel Lane equations are solved to obtain the scattering observables. The use of conventional proton and neutron densities significantly underestimates Fermi (forward-angle) cross-sections in agreement with findings by various other groups. However, we have found model-independent densities which provide a…
Beta-delayed proton emission from the neutron halo ground state of $^{11}$Be raised much attention due to the unusually high decay rate. It was argued that this may be due to the existence of a resonance just above the proton decay threshold. In this Letter, we use the lenses of real-energy continuum shell model to describe several observables including the Gamow-Teller rates for the $β^-$-delayed $α$ and proton decays, and argue that, within our model, the large $β^-{\rm p}$ branching ratio cannot be reconciled with other data.
Using a simple model based on the knowledge of spherical and deformed Woods-Saxon potentials, it is shown that the recent observation of halo phenomena in $^{29}$F can be interpreted as an evidence for the prolate deformation of the ground state of $^{29}$F. The prolate deformation is the result of the shell structure, which is unique in one-neutron resonant levels, in particular near degeneracy of the neutron 1$f_{7/2}$ and 2$p_{3/2}$ resonant levels, together with the strong preference of prolate shape by the proton number $Z$ = 9. On the other hand, in oxygen isotopes spherical shape is so …
The absolute differential cross section for small-angle proton elastic scattering on the proton-rich $^8$B nucleus has been measured in inverse kinematics for the first time. The experiment was performed using a secondary radioactive beam with an energy of 0.7 GeV/u at GSI, Darmstadt. The active target, namely hydrogen-filled time projection ionization chamber IKAR, was used to measure the energy, angle and vertex point of the recoil protons. The scattering angle of the projectiles was simultaneously determined by the tracking detectors. The measured differential cross section is analyzed on t…
Proton radii of $^{12-19}$C densities derived from first accurate charge changing cross section measurements at 900$A$ MeV with a carbon target are reported. A thick neutron surface evolves from $\sim$ 0.5 fm in $^{15}$C to $\sim$ 1 fm in $^{19}$C. The halo radius in $^{19}$C is found to be 6.4$\pm$0.7 fm as large as $^{11}$Li. Ab initio calculations based on chiral nucleon-nucleon and three-nucleon forces reproduce well the radii.
The $^{11}$Be neutron halo nucleus appears to decay into $^{10}$Be with a rate that exceeds expectations. Neutron disappearance into dark matter, beta decay of a halo neutron, or beta-delayed proton decay have been offered as explanations. In this work we study the latter option; we carry out shell model calculations and sequential decay analysis examining the beta-delayed proton decay going through a resonance in $^{11}$B. The narrow energy window, lack of states with sufficient spectroscopic strength, overwhelming alpha decay branch, all make reconciling the observed rate with beta-delayed p…
Electromagnetic strength functions of halo nuclei exhibit universal features that can be described in terms of characteristic scale parameters. For a nucleus with nucleon+core structure the reduced transition probability, as determined, e.g., by Coulomb dissociation experiments, shows a typical shape that depends on the nucleon separation energy and the orbital angular momenta in the initial and final states. The sensitivity to the final-state interaction (FSI) between the nucleon and the core can be studied systematically by varying the strength of the interaction in the continuum. In the cas…
The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean field approach.
Starting from chiral two-nucleon (2NF) and chiral three-nucleon (3NF) potentials, we present a detailed study of 17Ne, a Borromean system, with the Gamow shell model which can capture continuum effects. More precisely, we take advantage of the normal-ordering approach to include the 3NF and the Berggren representation to treat bound, resonant and continuum states on equal footing in a complex-momentum plane. In our framework, 3NF is essential to reproduce the Borromean structure of 17Ne, while the continuum is more crucial for the halo property of the nucleus. The two-proton halo structure is …
We report an improved low-energy extrapolation of the cross section for the process Beryllium-7+proton -> Boron-8+photon, which determines the Boron-8 neutrino flux from the Sun. Our extrapolant is derived from Halo Effective Field Theory (EFT) at next-to-leading order. We apply Bayesian methods to determine the EFT parameters and the low-energy S-factor, using measured cross sections and scattering lengths as inputs. Asymptotic normalization coefficients of Boron-8 are tightly constrained by existing radiative capture data, and contributions to the cross section beyond external direct capture…
The symmetry energy in nuclei is studied using a monopole-monopole two boby interaction which has an isospin dependent term. A Hartree theory is developed for this interaction which has an oscillator shell model basis with corresponding shell structure. The role of shell structure on the symmetry energy is then studied. We also find that the strength of the Heisenberg interaction is very important for understanding the difference between proton and neutron radii and features associated with halo nuclei. PACS numbers: 21.10.Sf, 21.65Cd, 21.65Ef
In this paper, we point out that a measurement of the charge radius of Boron-8 provides indirect access to the S-factor for radiative proton capture on Beryllium-7 at low energies. We use leading-order halo effective field theory to explore this correlation and we give a relation between the charge radius and the S-factor. Furthermore, we present important technical aspects relevant to the renormalization of pointlike P-wave interactions in the presence of a repulsive Coulomb interaction.
We calculate the differential cross sections for proton elastic scattering on the exotic halo nuclei $^6$He and $^8$He at energies around $\sim$0.7 GeV at the momentum transfers squared up to 0.30 (GeV/$c$)$^2$ and investigate the influence of the nucleon centre-of-mass correlations on the calculated cross sections. In particular, we show that the approximate account of the centre-of-mass correlations used previously considerably overestimates the cross sections at high values of the momentum transfer.
A dripline nucleus $^{22}$C is studied in a Borromean three-body model of $^{20}$C+$n$+$n$. The valence neutrons, interacting via a realistic potential, are constrained to be orthogonal to the occupied orbits in $^{20}$C. We obtain ample results supporting that $^{22}$C is an ideal $S$-wave two-neutron halo nucleus: The ground state is bound by 390-570 keV, the root mean square neutron and proton radii are 4.0 and 2.4 fm, and the two neutrons are predominantly in $(s_{1/2})^2$ orbits. The binding mechanism of $^{22}$C is discussed. One- and two-body density distributions elucidate the halo cha…
Although the neutron (n) does not carry a total electric charge, its charge and magnetization distributions represented in momentum space by the electromagnetic form factors, $F_1^{(n)} (q^2)$ and $F_2^{(n)} (q^2)$, lead to an electromagnetic potential of the neutron. Using this fact, we calculate the electromagnetic corrections to the binding energy, $B_d$, of the deuteron and a one neutron halo nucleus (11Be), by evaluating the neutron-proton and the neutron-charged core (10Be) potential, respectively. The correction to $B_d$ (~9 keV) is comparable to that arising due to the inclusion of the…
Assuming a~simple spherical relativistic mean field model of the nucleus, we estimate the width of the antiproton--neutron annihilation ($Γ_n$) and the width of antiproton--proton ($Γ_p$) annihilation, in an antiprotonic atom system. This allows us to determine the halo factor $f$, which is then discussed in the context of experimental data obtained in measurements recently done on LEAR utility at CERN. Another quantity which characterizes the deviation of the average nuclear densities ratio from the corresponding ratio of the homogeneous densities is introduced too. It was shown that it is al…
Ground state properties of proton-rich odd-$Z$ nuclei in the region $55\le Z \le 73$ are studied in the relativistic mean field (RMF) theory. The RMF equations are solved by using the expansion method in the Harmonic-Oscillator basis. In the particle-particle channel, we use the state-dependent BCS method with a zero-range $δ$-force, which has been proved to be effective even for neutron-rich nuclei. All the ground state properties, including the one-proton separation energies, the ground state deformations, the last occupied proton orbits and the locations of proton drip line, are calculated.…
We construct a formula for proton-nucleus total reaction cross section as a function of the mass and neutron excess of the target nucleus and the proton incident energy. We deduce the dependence of the cross section on the mass number and the proton incident energy from a simple argument involving the proton optical depth within the framework of a black sphere approximation of nuclei, while we describe the neutron excess dependence by introducing the density derivative of the symmetry energy, L, on the basis of a radius formula constructed from macroscopic nuclear models. We find that the cros…
Giant neutron halos in medium-heavy nuclei are studied in the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions. The appearance of such structures depends sensitively on the effective interaction adopted. This is illustrated by comparing the predictions of SLy4 and SkI4 in the Ca and Zr isotopic chains. The former force gives no halo effect, the latter predicts a neutron halo in the Zr chain with A>122 due to the weakly bound orbitals 3p1/2 and 3p3/2. The structure of the halo is analyzed in terms of the occupation probabilities of these orbitals and their partia…
Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as $1/A_c$, where $A_c$ is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account f…
The binding energies, shapes and sizes of even-even beta-stable nuclei with A >= 40 and a few chains of isotopes with Z=50, 56, 82, 94 protons and isotones with N=50, 82, 126 neutrons are analyzed. The average isospin dependence of the radii of protons and neutrons evaluated within the relativistic mean field theory is studied. A simple, phenomenological formula for neutron radii is proposed.
Reaction cross sections of carbon isotopes for proton scattering are calculated in large energy region. Density distributions of carbon isotopes are obtained from relativistic mean field results. Calculations are based on two procedures: the Glauber theory and relativistic impulse approximation, and results are compared with each other as well as with experimental data. A strong relationship between reaction cross section and root-mean-square radius is clearly shown for 12C using a model distribution.
We calculate the mean free path of protons and neutrons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. Those are obtained from calculations of the G-matrix including relativistic "Dirac" effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions may be helpful in conjunction with studies of rare isotopes.
We have studied the ground state properties (binding energy and charge radius) using relativistic mean filed formalism (RMF) for Mg-isotopes in the valley of stability to drip line region. The RMF densities have been analyzed in context of reaction dynamics. The calculated results of $^{24-40}$Mg+$^{12}$C reactions at projectile energy 240 AMeV using Glauber model with the conjunction of densities from relativistic mean field formalism are compared with experimental data. We found remarkable agreement of estimated values of reaction cross sections with experimental data except for $^{37}$Mg is…
