Structural Analysis of 23 O Through Single-Neutron Stripping Reaction

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1 Commun. Theor. Phys. (Beijing, China) 49 (008) pp c Chinese Physica Society Vo. 49, No. 4, Apri 15, 008 Structura Anaysis of 3 O Through Singe-Neutron Stripping Reaction Rajesh Kharab, 1, Ravinder Kumar, 1 Pardeep Singh, 1 and H.C. Sharma 1 Department of Physics, Kurukshetra University, Kurukshetra, Haryana , India Department of Appied Sciences, Haryana Coege of Technoogy and Management, Kaitha, Haryana , India (Received Apri 9, 007; Revised June 1, 007) Abstract We have studied the singe-neutron stripping reaction induced by 3 O on carbon target at beam energy of 7 MeV/A with a motive to anayze its ground state structure. The partia stripping cross sections as we as ongitudina momentum distribution of O core have been cacuated within the framework of the eikona approximation approach. Severa core-neutron spin couping configurations, corresponding to J π = 1 + as ground state spin parity of 3 O, aong with their suitabe admixtures have been considered. The major outcome of the present work is that the s and d admixed configuration with a arge contribution of s state seems to expain the ongitudina momentum distribution data more satisfactoriy. PACS numbers: 5.60.Gc, 5.70.Mn, 5.60.Dz Key words: stripping, hao nucei, admixed state 1 Introduction In the ast two decades the study of neutron/proton rich nucei ying cose to drip ines reveas exciting structura features of these nucei, quite different from the conventiona stabe nucei. The pioneering work of I. Tanihata et a. [1,] expored an exotic structure for these nucei frequenty referred to as nuceon hao. Basicay, this nove hao structure consists of a two-fod structure containing a core with norma nucear density and one or two diffused vaance nuceons. So far, the hao structure has been confirmed for various ight neutron/proton-rich nucei. [3 7] Recenty atest techniques in experimenta faciities provide fast track to the invention of heavier exotic nucei. In ast few years the avaiabiity of the high energy beams of neutron-rich nitrogen, oxygen and fuorine isotopes has made it possibe to expore their structura properties. The oxygen isotope with mass number 3 having a doube-cosed-she-pus-one-neutron structure is a key nuceus for understanding the structure of heavier neutron-rich isotopes. An intensive experimenta work has aready been devoted to investigating its unique structura features. [8 1] A these studies have confirmed the existence of one-neutron hao in 3 O nuceus. However, controversia resuts have been reported regarding its ground state structure. An experiment performed at GANIL [13] reported J π = 1/ + as the spin parity for 3 O ground state and ater revised to J π = 5/ + by another experiment preformed at RIKEN. [9] A more recent measurement at GSI once again supported spin parity of 1/ + for the 3 O ground state. [14] Severa observabes ike interaction cross section, ongitudina momentum distribution (LMD), and one or two neutron remova cross section have been measured and the resuts so obtained were interpreted within the framework of different theoretica modes to resove this controversy. In the present work we anayze, with a motive to determine orbita occupancy of vaance neutron in the ground state of 3 O, the one neutron remova cross section and the LMD of O core fragment emerging from the stripping on carbon target at 7 MeV/A beam energy within the framework of eikona approximation approach. The theoretica mode used is being described briefy in Sec.. The resuts are discussed in Sec. 3 whie section 4 contains important concusions. Theoretica Formaism The ground state of the projectie may be considered as a superposition of configurations of the form [Ic π n j ] Jπ, where Ic π represents the spin and parity of the core states and n j specify the quantum numbers of the singe partice wave function of the ast nuceon. The singe partice wave function of the ast nuceon is obtained by soving the concerned Schrödinger equation in a Woods Saxon potentia. The depth of the potentia is adjusted to reproduce the effective separation energy Sn eff = S n + Eex, c with Eex c being the excitation energy of the core state. When dynamica excitation and couping to the fina state of excited core states are negected then the reaction can popuate a given core state ony to the extent that there is a non-zero spectroscopic factor C S (Ic π, n j) in the projectie ground state. When more than one configurations contribute to this core state then tota one nuceon remova cross section is written as [15] σ 1n (I π c ) = n j C S (I π c, n j) σ sp (n j, S eff n ). (1) The tota incusive cross section for one neutron remova is obtained by summing over the cross sections to a core states. E-mai: kharabrajesh@rediffmai.com

2 No. 4 Structura Anaysis of 3 O Through Singe-Neutron Stripping Reaction 1005 The singe partice cross section σ sp (n j, S eff n ) consists of the foowing three terms σ sp (n j, S eff n ) = σ str sp (n j, S eff n ) + σ diff sp (n j, S eff n ) + σ c sp(n j, S eff n ), () where interference between the ast two terms has been negected. These terms correspond to the stripping of vaance nuceon, nucear diffraction dissociation, and Couomb dissociation processes, respectivey. In the present study, we concentrate ony on the nuceon stripping or absorption process and cacuate the tota cross section and ongitudina momentum distribution of the core fragment. Various theoretica approaches have been used to mode the nucear stripping reaction data. [15 1].1 Stripping Cross Section The tota stripping cross section, in the spirit of the spectator core mode, is given by [11] σ str sp (n j, Sn eff ) 1 = d J + 1 b φ k Ω str ψ J M, (3) k M where φ k are the scattering states and satisfy the foowing cosure reation, φ k φ k = 1. (4) k Combining Eqs. (3) and (4), we have σsp str (n j, Sn eff 1 ) = d J + 1 b Ω str ψ JM ψ JM. (5) M The ψ JM represents the ground state of the projectie and corresponds to the couping scheme [[ 1 ] j I c ] J. Foowing the anguar momentum couping rues, we may write [( ψ JM ( r, σ, ξ) = 1 ) j I ] c J Cm (1/) j m s m C j I cj m m I c M m, m s, m I c χ m Ic I c (ξ) χ m s 1/ (σ)r (r) Y m (ˆr). (6) Substitution of Eq. (6) into Eq. (5) aong with a itte anguar momentum agebra yieds the foowing expicit expression for singe partice stripping cross section σsp str (n j, Sn eff ) = 1 4π d b d s[1 S n ( b + s ) ] S c ( b ) dz R (r), (7) where (1 S n ( b + s) ) S c ( b) ( Ω str) represents the transition operator for neutron absorption with S c and S n as the S-matrices (or the profie function) of the coretarget and removed nuceon-target systems respectivey expressed as a function of their impact parameters. The neutron and core impact parameters aong with other coordinates are shown in Fig. 1. It is trivia to show that the bn and b c are reated to the reative coordinates r( s, z), between the core and the nuceon, and coordinate of the center of mass R of the projectie by the reation bn = R + A c A c + 1 s = b + s, bc = R 1 A c + 1 s = b. Fig. 1 Geometry of the probem. The forms of profie functions range from simpest extreme strong absorption back disk mode to diffused form based on the optica imit of eikona mode. In the present work, we treat the profie functions within the optica imit of eikona mode whereby these are defined by the ongitudina integration over the corresponding potentia [ S i (b i )=exp i ( dz V i b i )], h v + z i = n or c (8) with v as the beam veocity. The potentia V i is the fu optica potentia, which incudes the Couomb potentia and the rea and imaginary parts of the nucear potentia. The form of the nucear potentia is considered as the usua Woods Saxon form with voume and surface imaginary terms with parameters taken from Ref. []. However the spin orbit couping term, owing to the sma contribution, is negected. The optica potentia for core-target interaction is obtained by foding of nuceon-target interaction potentia V nt with the core density ρ c (x), V ct (r) = d xρ c (x) V nt ( r x ), where V nt ( r ) is the goba nuceon optica potentia. Usua harmonic osciator mode is empoyed to describe the core density ρ c (x), [3] ( x ] [ ( x ] ρ c (x) = ρ 0 [1 + α exp. (9) a) a) The parameter α is reated to a by the foowing expression α 0 a 0 α = a + 3α 0 (a a, (10) 0 )/

3 1006 Rajesh Kharab, Ravinder Kumar, Pardeep Singh, and H.C. Sharma Vo. 49 where a 0 = (a a p)a/(a 1) and α 0 = (Z )/3 with a p = r proton /3. The parameter ρ 0 is fixed at fm 3 whie the other free parameter a is adjusted to reproduce mean charge radius of the core nuceus, which comes out to be.3 fm for O core.. Longitudina Momentum Distribution The basic expression for the cross section differentia in momentum in stripping reaction is given by [4] ( dσ ) d k = d b dp str d (11) k with dp d k = 1 (π) 3Ĵ M m I c m s e i k r χ m s 1/ (σ) χm Ic I c (ξ) Ω ( b, s ) ψ J M ( r, σ, ξ). (1) Integration is taken over nuceon ( r, σ) and core spin (ξ) coordinates. Using Eq. (6), orthonorma properties of spin wave functions and appying some anguar momentum agebra one obtains dp d k = 1 (π) 3ˆ m d r e i k r Ω ( b, s )R (r) Y m (ˆr).(13) The ongitudina momentum distribution is now obtained by integrating it over a the transverse momenta. After performing this integration using d k exp[ k ( s s )] = (π) δ ( s s ) and combining the resuting expression with Eq. (11) we have ( dσ = dk z )str 1 d bd s [1 S n ( b+ s ) ] S c ( b) πˆ m dz e ikzz R ( s + z ) Y m (ˆr). (14) 3 Resuts and Discussion We have cacuated the singe neutron stripping cross section and ongitudina momentum distribution (LMD) of O fragment coming out from the breakup of 3 O on carbon target at a beam energy of 7 MeV/A. The main inputs needed in the cacuations are the radia part of the ground state wave function of the projectie and the profie functions corresponding to the neutron-target and core-target interactions. The determination of profie functions has aready been described in the pervious section. As far as ground state of 3 O is concerned there exists a arge ambiguity regarding its spin parity. Since most of the dedicated experiments favor an assignment of 1/ + as its ground state spin parity except a few pointing to its ground state as 5/ +, [9] we have aso assumed here 1/ + as its ground state spin parity and have considered ony those core-neutron spin couping configurations, which give a resutant of 1/ + and are shown in Tabe 1. It may be ceary seen in Tabe 1 that the remova of s orbita vaance neutron eads to the production of the core either in ground (0 + ) or in excited (0 + ) states whie that of d orbita neutron aways eads to excited +, 3 +, and + core states. The excitation energy of core (EC ex), effective separation energy (Sn eff ), aong with the spectroscopic factors taken from Ref. [5] corresponding to different possibe spin couping schemes of core with vaance neutron, are aso isted in Tabe 1. Since the spectroscopic factors greater than unity are inconsistent with present core pus singe neutron mode, we have performed the cacuations assuming 0.8 and 0. as the vaues of spectroscopic factors corresponding to the configurations having the vaance neutron in s and d orbita respectivey adding up the s and d wave strengths to unity. Tabe 1 Partia singe-neutron stripping cross sections for 1 C( 3 O, O +n)x reaction at 7 MeV/A incident energy corresponding to different core-neutron couping schemes for J π = + 1 as ground state spin parity of 3 O. Eex C (MeV) Seff n (MeV) Spin couping [core neutron] σ str (mb) C S FWHM of LMD (MeV/c) 0 (g.s.).74 [0 + s 1/ ] 1/ [0 + s 1/] 1/ [ + 1d 5/ ] 1/ [3 + 1d 5/ ] 1/ [ + 1d 5/] 1/ The radia part of the wave functions corresponding to each configuration is obtained by soving the concerned Schrödinger equation in a Woods Saxon potentia. The depth of the potentia is adjusted to reproduce the effective singe neutron separation energy whie the diffuseness and range parameter (, R 0 ) are fixed at 0.5 fm and.45 fm respectivey. These wave functions are used to cacuate the partia one-neutron stripping cross section. The

4 No. 4 Structura Anaysis of 3 O Through Singe-Neutron Stripping Reaction 1007 resuts so obtained are isted in Tabe 1 and impy that the stripping cross section decreases with increase in the core excitation energy. It may be ascribed to the increment in effective neutron separation energy as a resut of core excitation. Further, it is aso important to note that the stripping cross section is sighty smaer for [ + 1d 5/ ] 1/ + configuration than that for [0 + s 1/] 1/ + even though the Sn eff energy is smaer for the former. It may be attributed to the presence of a strong centrifuga barrier for [ + 1d 5/ ] 1/ + configuration. Figure depicts the cacuated LMD of O coming out from the stripping of 3 O on carbon target at 7 MeV/A beam energy aong with the corresponding data taken from Ref. [9]. The curves correspond to different core and neutron spin couping schemes given in Tabe 1. The peaks of a the curves are normaized to data peak for the sake of carity of comparison. The width corresponding to a these curves are isted in Tabe 1. It is cear from the tabe that a those configurations in which the vaance neutron occupies d orbita significanty overestimate the observed width 94±1 MeV/c of LMD whie the configuration corresponding to vaance neutron in s orbita sighty underestimates it. It strongy indicates that an admixed state with a arge contribution of s orbita occupancy may reproduce the data effectivey. and the resuts aong with the corresponding data are presented in Fig. 3. It may be ceary observed from Fig. 3 that a these configurations are equay consistent with the LMD data. Further, the vaues of the singe partice stripping cross sections come out to be 34.49, , and mb for 0.8[0 + + s 1/ ] + 0.[ + + 1d 5/ ], 0.8[0 + + s 1/ ]+0.[3 + +1d 5/ ] and 0.8[0 + +s 1/ ]+0.[ + +1d 5/] configurations respectivey, which are amost equa to each other. As a resut, the present core pus singe neutron treatment of 3 O is inadequate in the quantitative determination of the suitabe configuration for its ground state. Nevertheess, we may concude that ground state of 3 O is an admixture of s and d states with a arge contribution of s state. For quantitative description of 3 O ground state a core pus muti-nuceon mode woud be more appropriate but a proper reaction theory empoying it is sti acking. Fig. 3 The same as Fig. but for admixture of predominant [0 + +s 1/ ] ground state with different excited core states. The data points are taken from Ref. [9]. Fig. Longitudina momentum distribution of O coming out from the stripping of 3 O on carbon target at 7 MeV/A beam energy for different core-neutron spin couping configuration. The data points are taken from Ref. [9]. In order to find a suitabe admixed state for 3 O ground state, we consider the foowing core-neutron spin couping schemes 0.8[0 + +s 1/ ]+0.[ + +1d 5/ ], 0.8[0 + + s 1/ ]+0.[3 + +1d 5/ ] and 0.8[0 + +s 1/ ]+0.[ + +1d 5/]. Corresponding to these configurations the ongitudina momentum distributions of O core have been computed 4 Concusions The ground state of nuceus 3 O, extremey neutronrich nuceus, has been investigated through the oneneutron remova reaction on carbon target at 7 MeV/A incident energy within the framework of eikona approximation approach. Various possibe core-neutron spin couping configurations, corresponding to the widey adopted J π = 1 + ground state spin parity, aong with the admixtures of core excited states with the predominant ground state [0 + + s 1/ ] + 1/ have been used to anayze the observed LMD of O. Eventuay, ony admixtures of s and d configurations with the spectroscopic factors 0.8 and 0. have been found to reproduce the LMD data very we eading to this admixture as the most appropriate configurations for 3 O.

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