Main mechanisms in fragmentation of the exotic nucleus 6He

Main mechanisms in fragmentation of the exotic nucleus 6He

NUCLEAR PHYSICS A Nuclear Physics A567 (1994) 97-110 North-Holland Main mechanisms in fragmentation nucleus 6He A.A. Korsheninnikov ‘, T. Kobayashi...

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NUCLEAR PHYSICS A

Nuclear Physics A567 (1994) 97-110 North-Holland

Main mechanisms in fragmentation nucleus 6He A.A. Korsheninnikov

‘, T. Kobayashi

of the exotic

b

a The Kurchator Institute, 123 182 Moscow, Russian Federation b RIKEN, Hirosawa, Wako, Saitama 351-01, Japan Received (Revised

8 February 1993 11 May 1993)

Abstract The momentum distributions of cy-particles and neutrons from the fragmentation of ‘He at high energy are studied using a microscopically calculated ‘He wave function. Various fragmentation mechanisms are included in the calculation. A comparison with the experimental data shows that it is essential to consider (i) the n-target interaction, (ii) the n--(Y final-state interaction at the 5Hes.s, state and (iii) the motion of particles (n and 4He) in ‘He.

1. Introduction The development of secondary radioactive beams has enabled intensive experimental studies on the structure of light neutron-rich nuclei [l-5]. The studies included: (i) measurements of interaction cross sections, fragmentation and electromagnetic dissociation cross sections and (ii> measurements of momentum spectra of projectile fragments. The measurements of the first type (integrated cross sections) gave information on global characteristics of exotic nuclei, e.g., matter radii, the existence of an extended neutron distribution called “neutron halo”. Differential distributions of fragments can provide information on details of the structure, e.g., correlations in the neutron halo. However, in this case, in addition to the unknown nuclear structure, another uncertainty exists, namely the fragmentation mechanism. In this paper we study the latter problem and analyze experimental data of the 6He fragmentation. As it was pointed out in ref. [61, this nucleus is expected to provide a good case to clarify the fragmentation mechanism because microscopically calculated 6He wave functions are available [7-lo]. The 6He fragmentation at high energies was experimentally investigated in refs. [3,5]. In ref. [3] the transverse-momentum distribution of a-particles was measured at 0.4 A . GeV. In ref. [51 the transverse-momentum distribution of neutrons was measured in coincidence with a-particles at 0.8 A . GeV. 03759474/94/$07.00

0 1994 - Elsevier

SSDI 0375-9474(93)E0273-B

Science

B.V. All rights reserved

A.A. Korsheninnikor~, T. Kohayushi / Fragmentation of the exotic nucleus “He

Microscopic number

calculations

of different

son of the results coordinate-space

of the ‘He nucleus

three-body obtained Faddeev

were made

((u + n + n) approaches in the hyperspherical

equation

method

in the framework

[7-lo].

harmonic

[lo] demonstrated

A careful method that

are practically identical [lo]. In ref. [S] the results of the hyperspherical method were found to be close to the results obtained by the variational

of a

compari-

[8] and the both

results

harmonic approach

method [7]. In the present paper we use the ‘He wave function from the hyperspherical harmonic method [8]. The latter reproduces many characters of A = 6 nuclei (binding energies, P-decay probabilities, cross sections of charge exchange reactions, electromagnetic form factors, radii and other values [8,10-141). In addition, ‘He attracts attention due to its specific structure. The microscopic calculations revealed the extended valence neutron distribution, which was called “neutron halo” in refs. [15,8]. Recently this result was experimentally confirmed in ref. [16], where the phenomenon was called “thick neutron skin”. The most fascinating aspect is the prediction of exotic correlations in the neutron halo. The expected correlations are the di-neutron spatial configuration (one neutron is close to another) and the cigar-like configuration (neutrons are on opposite sides of a). This result, which was found for the first time in ref. [7], was obtained also in different theoretical approaches [S,lO]. The correlations are interconnected with angular momenta dominated in the three-particle system, and the Pauli principle (Pauli focusing quantum effect [17,8]). Three-particle correlations of this nature were experimentally observed for nuclear states unstable with respect to a threeparticle decay [ 18,191.

2. Fragmentation

of the 6He nucleus

Using the ‘He wave function [8], we analyze the momentum distributions of a-particles and neutrons measured in refs. [3,5] and investigate the fragmentation mechanism. The mechanisms included in the calculation are illustrated in Fig. 1: (a) sudden approximation, (b) scattering of a neutron in ‘He on a target, (cl the n-target scattering and final-state interaction n + a, (d) the a-target scattering and final-state interaction n + n. These mechanisms are considered because of the specific shape of the experimental spectra. 2.1. Sudden approximation During the last 20 years many investigations of fragmentation processes of stable nuclei demonstrated that, in a great number of cases, fragment momentum distributions reflect the momentum distribution of nucleons in a projectile [20-251. This sudden approximation (or Serber model) was used in ref. [26] to predict distributions of LYand n from the ‘He fragmentation at high energy. Use was made

A.A. Korsheninnikou, T. Kobayashi / Fragmentation of the exotic nucleus 6He

A

‘e;

99

Sudden approximation

a 6He

n

@

6He

The ,!*C scattering

n

B

n 12

%

C

fWC

12C

FSI n-a

C

the n-‘% scattering

‘e”

D

and

FSI n-n and the crJ2C scattering a 12

C

Fig. 1. Fragmentation processes investigated in this paper: (a) sudden approximation; scattering; (c) the n-‘*C scattering and final-state interaction n-a; (d) the (w-‘*C final-state interaction n-n.

of the wave function obtained in ref. [8]. In Fig. 2 the momentum distribution of o-particles (curve 1) is compared data from 6He + 12C + cr + X at 0.4 A . GeV [3]. One can between this calculation and the experimental data. However, as one can see in Fig. 3, the calculated * distribution of neutrons (curve 1) differs drastically from the

(b) the n-“C scattering and

calculated transversewith the experimental see a good agreement transverse-momentum experimental data for

* In ref. [5] the py momentum acceptance was limited to - 120 < p, < 120 MeV/c. In the present paper all calculations of the p, transverse-momentum distributions of neutrons are carried out using experimental acceptance.

100

A.A. KorsheninnikoL, T. Kobayashi / Fragmentation of the exotic nucleus 6He

600 600 400 200 0 1400

0 P,. UN/C

-200

200

400

Fig. 2. The o-particle transverse-momentum distributions calculated (curve 1) and for the process in fig. lc (curve 2). Experimental

in the sudden approximation data are from ref. [3].

‘He + i2C + n + (Y+ X L.51.It shows a strong influence of the projectile fragmentation mechanism. The experimental neutron distribution shows two-component-like shape, which is clearly seen in Fig. 4 (logarithmic scale). Broader components at the bottom were observed in the all-neutron distributions from fragmentation of various projectiles ?He, sHe, 9Li, “Li) studied in ref. [.5]. The broad component widths are almost the same for all projectiles. Such a general feature in the neutron distribution is considered to be due to the neutron-target interaction. Therefore, in the next section we consider the scattering of a neutron in ‘jHe on a target. This process is illustrated in Fig. lb. 2.2. Neutron

scattering

2.2.1. Neutron-target

interaction

To describe neutron scattering on a carbon following amplitude [27] known in the Glauber

target (F,_, in Fig. lb), we use the theory for nucleon elastic scattering

2500 2000

500 n -200

-150

-100

-50 P,. usv/e

0

50

Fig. 3. The neutron transverse-momentum distributions calculated in the sudden approximation (curve 1) and for the process in Fig. lc (curve 2; the case of neutron non-scattered on target). Experimental data are from ref. [S].

A.A. Korsheninnikou, T. Kobayashi / Fragmentation of the exotic nucleus 6He

-200

-150

-100

-50 P,. usv/e

101

50

0

Fig. 4. The neutron transverse-momentum distributions (logarithmic scale) calculated for the neutrontarget scattering (curve 1) and for the neutron-target scattering with consideration of neutron motion in ‘He (curve 2). Experimental data are irom ref. [S].

on a target

that has the gaussian A

FChdq)

N

eq”4Au2n~,

shape density:

(-)“yLf! n(~

_

nj

(1 + 2&2)q2 Xexp

[

4a2n

n-l

a2(1 -iy)a ,,,

. .

24

+

2a2P2)

I

1’

(1)

where q is a two-dimensional vector for momentum transfer, which is perpendicular to the axis of collision, A is the target mass number, (Y is the parameter connected with the target matter radius R as a2 = $Re2 (for carbon R = 2.35 fm, which corresponds [28] to the r.m.s. charge radius 2.47 fm [29]); p, y, u are parameters of the nucleon-nucleon amplitude [30]. The first exponent in Eq. (1) reflects a recoil of the target nucleus. The parameter n is the number of target nucleons involved in scattering. The transverse-momentum

distribution

of neutrons

scattered

on a carbon

tar-

get, &&_(qx) = da/dqx - / I FGlauber I 2 dq,, is presented in Fig. 4 by curve 1. The shape of the distribution is determined by IZ = 1 in Eq. (11, which corresponds to scattering on one target nucleon. Such a result is well known from a number of studies of nucleon scattering on light targets at energies about 1 GeV. The width of the II = 1 component is predominantly determined by a2, i.e., by the carbon radius. Terms with n > 1 give contributions that are smaller by a several orders of magnitude and become important only at momentum higher than in Fig. 4. Inelastic processes have similar behavior, as is known from the proton-scattering studies [30,31]. One can see in Fig. 4, that such a pure Glauber calculation (curve 1 in Fig. 4) gives a smaller width than the broad component of the experimental distribution.

A.A. Korsheninnikoo, T. Kobayashi / Fragmentation of the exotic nucleus “He

102

2.2.2. Neutron motion in 6He In the reaction under consideration, 6He nucleus. internal q,),

,ps

The observed

motion =

the following

the scattered

transverse-momentum

in ‘He (kin”)

and the momentum

k, + k;‘aube’. Therefore, product:

neutron

was initially

in the

(k,“‘“) is the sum of the neutron

the observed

transfer

by the target (kFlauher =

distribution

has to be written

as

where Ifir,, describes the internal neutron motion in 6He (sect. 2.1). It is determined by the Fourier transform of the ‘He wave function and is presented in Fig. 3 by curve 1. The formula (2) which was written intuitively can be derived in the following way. Using plane waves in the entrance and exit channels, we obtain the amplitude for process in Fig. lb

F”-sm N / e-‘(PR+p~r~fPZ’~)t(rn,~c)~~sHe(~,, where

R = rC-bFle,

P =pC-hHe,

rl = r,,-“+

r2) eipoR dR dr,

p1 -I)~,_“~~,

r2 = m2_“,

dr,,

(3)

p2 = Pi,_,;

r ,_, is the distance between particle “i” and center of mass of “j”; pi_j is the conjugate momentum of relative motion of “i” and center of mass of “j”; p,, is the momentum of relative motion of “C and ‘He in the entrance channel. In Eq. (3) t(rn,_c> describes neutron-target interaction, ?PhHe(r”,_“Za, r,Z_,) is the three-particle (a + n + n) wave function of ‘He. With a little algebra, Eq. (3) becomes

where

f,mc(Ap,,_c>

is the neutron-target scattering amplitude with the argument can be rearranged to the form of the AP,,_, = -pCmbHe fp,,. The latter argument transfer momentum in the scattering AP”,~~ =P”,~~ -$n,_C, where in,_c is the momentum of relative motion of neutron and carbon before scattering. The second of the 6He wave factor in Eq. (4), &He(fin,_n2a, p,,_,>, is the Fourier transform function with the argument fin,_,,, = (pC_eHe -pJ(m, + m,)/(2m. + ma> + The value fi,,_,,, P”,~n,, (m, and m, are the masses of neutron and a-particle). is the momentum of neutron in the 6He center of mass before the scattering. The momenta Ap,,_, and fin,_,,, are related by AP,,_~ = k,, - khHemn/(2mn + m,) where k are momenta of particles in the ‘He + “C center of mass, -f%-“za, khHe = -klz, = -po. If we integrate the squared amplitude (4) over unobserved variables in the experiment and use Eq. (1) for fn&Apn,mc), we obtain Eq. (2). It is noted here that energy conservation is neglected as usual in the Glauber theory.

A.A. Korsheninnikoq

T. Kobayashi / Fragmentation of the exotic nucleus 6He

103

2.2.3. Comparison with experimental data The result calculated by Eq. (2) is presented in Fig. 4 by curve describes well the broad component in the experimental neutron Thus, the broad experimental the projectile by the target. is important to understand

component

is explained

The initial motion the spectrum.

by scattering

of this neutron

2. This curve distribution. of a neutron

in

in the ‘He projectile

The process under consideration does not change the a-particle transversemomentum distribution from that obtained in the sudden approximation in sect. 2.1 (curve 1 in Fig. 2). The same is true for the spectrum of the neutron that was not scattered by the target. Therefore we still have the curve 1 in Fig. 3, which disagrees with the experimental data. Between the pair of spectators n + GJ, a well-pronounced resonance 5He(iP> exists, which can modify the momentum distribution due to final-state interaction. In ref. [32], using an example of the theoretical investigation of the “Li fragmentation, it was demonstrated that the momentum distribution differs significantly when the final-state interaction is included. In the next section we consider the effect of final-state interaction. The process is illustrated in Fig. lc. 2.3. N-a

final-state interaction

2.3.1. Model To consider

the process

to the following

Fn-scat

+ FSI

in Fig. lc instead

of that in Fig. lb, we modified

Eq. (4)

form: -f,_c(

&n,-c)#+,e(

A-,,,,

P,,~a)f+a(

pn,-a) 7

where f,,_,(p,,~,) describes the n--(Y attraction. Multiplication by f,,_, in Eq. (5) corresponds to a form of the Watson-Migdal model, which is often used for a treatment of the nucleon-nucleon final-state interaction. Because the n--(Y interaction was intensively studied, the R-matrix formalism is available to describe the phase 6/i in f:l, - e % sin S,j/p. We use the standard R-function R,j = Y~/(E~~ - E) + Rt with parameters from ref. [33]. These parameters allowed us to reproduce well various experimental data on the n--(Y scattering, such as partial phase shifts, the n--(Y angular distributions, energy dependence of total cross section, analyzing powers [33]. We omitted in Eq. (5) the specification of the n--(Y orbital and total angular momenta, 1 and j, just to make the model more transparent. In practice, however, it is necessary to take into account the fact that the n--cy final-state interaction depends strongly on 1 and j because of the existence of resonance, e.g., 1 = 1, j = 5 (ground state of 5He). In other words, in Eq. (5) the f,,_, component with given Zj Ij. The ‘He wave function follows the component of &ne with the corresponding

104

A.A. Korsheninnikoc,

that was calculated

T. Kobayashi / Fragmentation of the exotic nucleus 6He

in ref. [S] and used in ref. [26] for the fragmentation

the sudden approximation was written in a different convert this to the form required in Eq. (5).

representation,

study in

and we should

2.3.2. “He waue function The ‘He

wave function

was calculated

in ref. [S] in the (n-n,

Ly-nn) transla-

tional invariant set of Jacobi coordinates for the coupling of angular momenta I[[I,_,I,_,,lL[~~lSlJ= 0) (J= 0 is the “He spin, S is summary spin of two neutrons, I,_, and I,_,, are angular momenta between two neutrons and between their center of mass and a-particle, respectively). We need to transfer the wave function in the (n-a, n-na) Jacobi coordinates and coupling of angular momenta

I~~~“_,~l~~~“_“,~l~l~ = 0). The wave function

in momentum

representation

is

where 1 = I,_, = I,_,,; K and {fly)} = {0”‘, nj_kn,_jk} are hyperspherical variables which are connected with reduced Jacobi momenta qjmk =P,_~/v~ and qi_jk = Pimlk/~~

by q&

+qLjk

=

K2,

qjmk =

K

sin tP,

ql_jk =

K

cos

e(‘);

A,..

are

reduced mass numbers; x are hypermomentum functions in numerical form, which were calculated in ref. [S]; Yi;,,, are hyperspherical harmonics; 0, are spin functions for two neutrons. In Eq. (6) I is even for S = 0 and odd for S = 1 (antisymmetry relative to the neutron permutation). To convert Eq. (6) in the (n-a, n-na) Jacobi coordinates, we use Reinal-Revai coefficients, YkiM(L?(2:I)) = C,,(I’ 1’ I I1jKL Ykl’,(fl$j)). Transition from the I[[IIlL[~~lSlJ = 0) coupling scheme to the I[[l$lj[f$]j]J = 0) one is done with the help of 9j-symbols. The squared wave function becomes

(the summation runs over KK’LL’jj’l n _ nI’n _ ” 1n_a 1’” _CX)v., are spin projections of (‘+‘/2,1+1/2)(cos 20) are o-de_ two neutrons). In Eq. (7) F;(0) = NA sin’8 cos’0 .PCKPZ1),z pendent parts of Y~~M(P~“sb’ and iVk are Jacobi polynomials and normalization

A.A. K~rsheninni~~~, T. K~bayashi f Fra~~~ntati~n

of the exotic nucleus 6He

10.5

factors). Angular functions are

G/%fi)=

_JzC( -)A[(ror~o~Ao)]2[w(j~~f~; ~h)]2P*(cos i--

(4T)2

79)

A

(8)

and P, are Clebsch-Gordan and Racah coefficients and Legendre polynomials). In order to take into account the n--(Yfinal-state interaction, we should formally consider the angular-dependent n--cy amplitudes Fz, =f~~,(p,~,)Pt(n~_,n,_,) with the intermediate momentum PA-_, and in Eq. (51, use ~~~~(~~~-“~~, p&J integrate over dnLz_,(pJz_, =p,,_,>. The dependence of #eHe on n’,*_,iis contained in the spherical harmonics Y,,. After expanding P, in Fz, with the help of “addition theorem” P,(n~_,n,_,) = 4~/~~mYr~(n:,_,)Y~,(n,_,), integration over dnh*-a becomes trivial because Y,, are orthonormal. In Eq. (5) this reduction of dependence on n& was taken into account. Therefore, for the n--(Y final-state interaction we have the same angular functions (8). For transition from Eq. (7) to the final-state interaction model of type (51 we need onIy to replace !PL by ‘Pkfjl,, where fil, are normalized to keep partial normalizations of processes with given jl. Finally, the “He wave function was found predominantly to have the p3,2 state of the n--Lyrelative motion (- 90% of the wave function norm). It is in agreement with the usual shell-model picture. In particular, the main terms with hypermomentum K = 2, which exhaust 92% of the complete wave function, contain the p3,2 state with weight of 95%. Because of this, the process in Fig. lc is mainly determined by the n-a: final-state interaction at the resonance 5Heg.S..The role of other states of the n-a! relative motion, e.g., pi/z, is negligible. 2.3.3. Comparison with experimental data The result is shown in Fig. 3 by curve 2. The result differs from the previously discussed sudden approximation (curve 1 in Fig. 3). As it is seen in Fig. 3, consideration of the internal motion followed by the n--cy final-state interaction describes well the narrow peak observed in the experimental neutron distribution. The predominant process is the n--cy final-state interaction at the j = 5 resonance 5Heg.S: For the neutron scattered by the target, the result does not differ from the above obtained curve 2 in Fig. 4. Considering the diagram in Fig. lc for both neutrons, one scattered by the target and the other, we can describe the whole experimental neutron distribution, as it is shown by curve 1 in Fig. 5. The ratio * of

l

This ratio was the only free parameter of counts in the measured spectra).

in this paper

(of course,

besides

normalization

to the number

106

A.A. Korsheninnikou, T Kobayashi / Fragmentation of the exotic nucleus 6He

2500 2000

j

1500

s 1000 500 0 -200 Fig. 5. The neutron

-150

-100

-50 PX.kV/0

0

50

transverse-momentum distributions calculated for the process and in Fig. Id (curve 2). Experimental data are from ref. [5].

in Fig. lc (cuwe

1)

yields for the narrow and the broad components in the neutron distribution differs only by 15% from unity which corresponds to the conservation of number of neutrons in the process in Fig. lc (the narrow component is larger). In particular, this difference can be attributed to the following. To get curve 1 in Fig. 5, we used for simplicity the direct sum of the narrow and the broad components and neglected possible interference effects. In any case the difference is small and ratio of integrals is reasonable. Calculated distribution of a-particles for the process (Fig. lc) is presented in Fig. 2 by curve 2. Difference between this curve and the result for sudden approximation (curve 1 in Fig. 2) is small. As it is seen in Fig. 2, the process in Fig. lc is in good agreement with the experimental a-particle distribution also. 2.4. Scattering

of a-particle

For completeness, in addition to the processes in Figs. lb and lc with neutron scattering on a target, we should consider the scattering of a-particle on the target. In this case two neutrons from 6He are spectators. If they are emitted with I n_n = 0, their motion is influenced by the n-n final-state interaction. The process is illustrated in Fig. Id. 2.4.1. Model By analogy

with Eq. (5), the model

F,-scattt~s~ -f,-c(

where

for the process

in Fig. Id is

&a_c)4~,e( 6,-m, P,-n)fn-k’n-n),

f,_,(p,_,) describes the n-n attraction in the singlet state and influences components with I,-, = 0. We use the effective-range expansion for the 4~ f,_,(p,_,> with scattering length unmn = - 16 fm and - 24 fm. In these two cases the difference between results is negligible. The remaining parameters of the

A.A. Korsheninnikou, T. Kobayashi / Fragmentation of the exotic nucleus 6He

effective-range

expansion

were

taken

from

ref. [34]. The

practically do not depend on these parameters. The (jHe wave function representation required calculation

is similar

final-state interaction. I[[I,_,1,_,,]L[~~]S]J

to the

procedure

which

results

107

of calculations

in Eq. (9) is the form (6). The was

used

before

for

the

n--cy

The angular functions in the current coupling scheme = 0) differ from Eq. (8). The expression for them was

derived in ref. [261. To calculate the distribution of neutrons, we omitted in Eq. (9) the term f,_c(Ap,_c). The latter does not select any narrow range over the a-particle energy in the center of mass of ‘He and, as a result, over the energy of relative motion of two neutrons E,_, and has no influence on the neutron distribution. 2.4.2. Comparison with experimental data The neutron distribution calculated for the process in Fig. Id is presented by curve 2 in Fig. 5. The width of the curve is determined by the motion of the center of mass of two neutrons in 6He and by the n-n final-state interaction. The latter is characterized by a low-energy peak followed by a long tail at higher E,_,. As one can see in Fig. 5, the calculated shape is not similar to the experimental distribution. This means that the process in Fig. Id, the a-scattering on the target, is suppressed. The same can be seen from the a-spectrum in Fig. 2 where the curve 2, which corresponds to the process in Fig. lc, is already very close to the experimental data. In other words, in Fig. 2 there is no space for significant contribution from a broad component corresponding to a-particles scattered on the target l. Suppression of the process in Fig. Id very roughly can be attributed to the following. We compared the squared sum of matter radii of a-particle and “C (1.49 fm and 2.35 fm, respectively) with the squared sum of the “C matter radius and the radius of valence neutron in 6He (3.55 fm according to the calculation [S]) and then took into account that in the cz + 12C scattering geelastic- icttota, [35]. The result shows that the process in Fig. Id is suppressed in comparison with the process

in Fig. lc by a factor

- 7. We also made the following

rough estimation.

Using uttota, for n + 12C and ceelastic for LY+ 12C, we considered the “mean free path” of i2C in the 6He nucleus. The density distribution of ‘He was presented as

* The estimated half-width on half-height for this component equals 140 MeV/c. The corresponding calculation for a-particles from the process in Fig. Id was carried out with the help of model (9). The term f,_c in Eq. (9) was approximated in the following way. Using Eq. (l), we obtained the nucleon-cr scattering amplitude as the main component n = 1. The amplitude has a gaussian shape as well as the nucleon-nucleon amplitude parametrisation which was used in ref. [27] to derive Eq. (1). We can apply Eq. (1) the second time to calculate the a-carbon scattering, if we replace the nucleon-nucleon amplitude parameters by the nucleon-(Y parameters. Considering again only the n = 1 term in Eq. (l), we need only the parameter of width p. This is that parameter, which we obtained before, when we applied Eq. (1) for the nucleon-o scattering.

108

A.A. Korsheninnikou,

two spheres r.m.s.

for the a-core

characteristics

T. Kobayashi

and valence

of 6He

neutron scattering dominates, ing is about 10 times lower.

/ Fragmentation

[Sl. This

neutrons estimation

and the contribution

of the exotic nucleus ‘He

with radii which correspond shows

that

the

of the process

process

to with

with a-scatter-

2.5. Correlations in ‘He In order

to describe

experimental

Fig. lc and take into account tion and the particle internal

data, it is essential

to consider

the process

in

the n-target scattering, the n--(Y final-state interacmotion in “He. The latter is described by the ‘jHe

wave function. As it was mentioned in the Introduction, various calculations predict the specific (Y+ n + n correlations in 6He. For the sensitivity of transverse-momentum distributions to the (Y+ n + n we make calculations for the process in Fig. lc, in which we neglect tions. In formulas (6) and (7) for the “He wave function, the cy + n + n

microscopic investigating correlations, the correlacorrelations

are connected most directly with the functions P;(0), which are o-dependent parts for “structureless 6He”, of hyperspherical harmonics Y,&,,,. To make a caricature we replace V;(0) with the constants (preserving all the required normalizations; halo, density all other characteristics of 6He, e.g., radius, existence of neutron distribution over hyperradius, remains the same as before). The resultant neutron distribution describes experimental data and does not differ from the curve 1 in Fig. 5, which shows the result of the strict calculation taking into account the (Y+ n + n correlations. The result of “structureless” calculation for the a-particle distribution differs from the experimental data and the curve 2 in Fig. 2. The width at half-maximum of “structureless” curve is wider by 30% than the experimental width. Such a different sensitivity of the neutron and the a-particle distributions to the CY+ n + n correlations is closely related with the type of correlations in ‘He. Namely, the correlations in “He are very pronounced over the (a-nn, n-n) Jacobi variables, but distributions over the (n-cwn, cu-n> variables are smooth. The correlations are strongly integrated in a transverse-momentum and they are expected to be observed more evidently in correlation

distribution, experiments.

3. Summary The transverse-momentum distributions mentation of the exotic nucleus ‘He were cally calculated wave function of ‘He. various fragmentation mechanisms. To experimental spectra, we investigated the

of a-particles and neutrons from fraganalyzed with the help of a microscopiSimple models were used to consider understand the specific shape of the fragmentation mechanisms illustrated in

A.A. Korsheninnikou, T. Kobayashi / Fragmentation of the exotic nucleus 6He

109

Fig. 1 - from the sudden approximation to more complicated processes with final-state interactions and fragment-target scatterings. The experimental data were found to be reproduced by the process in Fig. lc. The process includes the following ingredients: (i) motion of neutrons and a-particle in 6He; (ii) the n--cy final-state interaction at the 5Heg,S,state; (iii) the n-target interaction. The experimental a-spectrum was found to reflect the exotic (Y+ n + n correlations in 6He. For further progress, it is desirable to carry out correlation experiments and model-less theoretical investigations.

We are grateful to Prof. I. Tanihata for useful comments and help in preparation of this paper. One of the authors, A.A.K., is thankful for the hospitality to RIKEN where this work was done.

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