- Email: [email protected]
Study of halo structure in light nuclei with a multicluster model
N ELSEVIER
NUCLEAR PHYSICSA Nuclear Physics A588 (1995) 15c--22c
Study of hMo structure
in light nuclei with a multicluster
model
Y. Suzuki ~ * , K. Arai u , y . Ohbayasi b and K. Varga c d ~Physics Department, Niigata University, Niigata 950-21, Japan bGraduate School of Science and Technology, Niigata University, Niigata 950-21, Japan qnstitute of Nuclear Research of the Hungarian Academy of Sciences, Debrecen, P.O. Box 51, H-4001, Hungary dRIKEN, Hirosawa, Wako, Saitama 351-01, Japan Detailed structure of light exotic nuclei is described with a multicluster model comprising c~, t, aHe, p and n clusters. The multicluster dynamics is fully taken into account with the stochastic variational method. The model enables us to describe the non-uniform and spatially extended density distribution of the halo structure. It is discussed that light stable nuclei have halo-like structure as the isospin increases. 1. I N T R O D U C T I O N The neutron halo or skin structure has been disclosed near the neutron drip line of light nuclei[i,2], e.g., in the ground states of 6'SHe, mLi, m'14Be, and 17B. The halo structure is characterized by its very low density distribution extending far spatially between the core and halo parts. For a detailed description of such non-uniform halo structure a theory needs to pay attention to (i) asymptotic behavior relevant to the particle threshold and (ii) various types of correlation between the core and the halo neutrons as well as (iii) the polarizability or deformability of the core. A microscopic multicluster model has been developed[3] to describe light exotic nuclei as an aggregate of clusters such as a, t, 3He, p and n. So far the cluster model has not been used much to describe systems containing more than two clusters. However, three or more clusters must be considered for a complete description of the exotic nuclei. For example one has to go beyond the 6 H e + n + n - t y p e or a+(2n)+(2n)-type three-body models to give a realistic description of SHe. Since the dynamics of the multicluster system becomes rather complicated, we have developed a very efficient procedure to select important basis wave functions, the so-called stochastic variational method [3,4]. In contrast to the multicluster approach the mean field theory or its approximate version of the antisymmetrized molecular dynamics[5] may give an explanation for the bulk property of nuclei but has limitation in well describing individual properties of these light exotic nuclei. *Supported by a Grant-in Aid for Scientific Research (No. 05243102 and No. 06640381) of Ministry of Education , Science and Culture(Japan). 0375-9474/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved. SSDI 0375-9474(95)00093-3
Y. Suzuki et aLI Nuclear Physics A588 (1995) 15c-22c
16c
The wave functions obtained in the multicluster model calculation can be used to discuss how well we understand the halo structure. The importance of both the halo neutron correlation and the spatial extension is revealed in the analysis of the momentum distributions of the fragment in the breakup reactions of mLi and 6He, and the energy spectrum of the ~-delayed deuteron emission of 6He. To inquire of universal existence of the halo structure in nuclei other than the drip line nuclei, the structure of the 3.563 MeV 0 + state of 6Li, an analog of the 6He ground state, is investigated with the a+p+n three-body model and is shown to have density distribution spatially extended well enough to be called a proton-neutron halo around the a-particle. 2. A M I C R O S C O P I C M U L T I C L U S T E R M O D E L W I T H A S T O C H A S T I C VARIATIONAL METHOD The Hamiltonian used consists of the kinetic energy and the effective two-body internucleon potential of Minnesota type. The center-of-mass motion is properly treated. A trial wave function is built up as a sum over various cluster arrangements #, each associated with a particular set of intercluster Jacobi coordinates P f l , ' " , P~n' The wave function of the intercluster motion is described by a linear combination of nodeless harmonic oscillator functions of different size parameters: Fkt~(pP) = [ ~ - ~ - ~ T ! !
]
(p~)texp[--u~k(p~)2]Yt,,,(~),
(1)
where u~ is the kth size parameter of the ith relative motion in the cluster arrangement #. The variational trial function is thus given by
o--Z #
Z; S,(II...I,),L
"
• F"
"
,
(2)
K
where A is the intercluster antisymmetrizer which assures a fully microscopic description and Os is a vector-coupled product of the intrinsic wave function of the clusters and the spin-isospin functions and K stands for the set of the indices {kl, ..., kn} of the size parameters. The function FK(t,...l~)L is a vector-coupled product of the intercluster relative motion functions r~,,~, ( P 0 . The details can be found in Refs. [3,6-8]. The trial wave function of Eq.(2) contains a great number of terms, due riot only to the different arrangements and angular momenta but, especially, to the various size parameters. Owing to this it can describe both various types of correlation and the spatially extended halo structure. Although the use of a particular rearrangement channel in principle constitutes a complete basis, we have a number of examples which show that the energy convergence in the case is extremely slow and that the use of various rearrangement channels is superior[6]. The most efficient procedure of selecting the basis states while keeping the dimension of the basis feasible is the stochastic variational method: We generate size parameter sets by choosing randomly from an interval which corresponds to the physically important region. The parameter sets that satisfy an admittance condition are selected to be basis states. We admit a candidate if it, together with the previously selected basis states, lowers the energy more than a preset value.
Y. Suzuki et el. I Nuclear Physics A588 (1995) 15c-22c
17c
3. R E S U L T S 3.1. 6He and SHe The structure of 6He and SHe was described with the a+n+n and a + n + n + n + n models, respectively[6]. For the five-body description of SHe the following six channels were ineluded: {[(an)n]n}u, [(an)n](nn), [a(nn)](nn), {[a(nn)]n}n, {[(an)in]in}n, {[(a(nn)]n}n, The lower indices indicate that /=1 partial waves were taken in the corresponding relative motion. Most important channels of 7He+n and 6He+2n are naturally included in this model together with the possible polarizability of 6'THe. The calculated proton and neutron densities are shown in Fig. 1, confirming the thick neutron cloud.
~1°2~-
0
\ \,,~---(neu~o.)[ .~I0: iton)
,
1
2
3 r(fm)
4
5
0
1
2 3 r(fm)
4
5
Figure 1. Empirical(short-dashed curve) [9] and theoretical(solid curve) proton and neutron density of 6He and SHe. ,._., 1.6
1.6[
(a) 6He
>. 1.2
.,... 0 ' ~ 0.8
._o.o.I
/."
•
,.ID
/
~ o.4
\
I
0.0 - 200
I -100
I 0
I I00
transverse momemtum (MeV/c)
200
-200
-I00
\ 0
100
200
transeverse momemtum (MeV/c)
Figure 2. Experimental(solid curve) and theoretical(dashed curve) momentum distributions of 4He in 12C(6He,4He) reaction and 6He in 12C(SHe,6He) reaction.
18c
Y. Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
The obtained wave functions can be tested with physical observables. It is convenient to define the two-neutron spectroscopic amplitude g(r,R)
A! ) 1/2 (A--~!1!1! (kI/A-2He(~(pl--r)5(P2--R)I~A"°)"
=
(3)
As shown in Ref.[6] it can be used to calculate the momentum distribution of the fragment and the energy spectrum of the/3-delayed particle emission. Fig. 2 compares theory with experiment[10] for the momentum distributions of the 4He fragment in the (6He, 4He) reaction and of the 6He fragment in the (SHe, 6He) reaction. The agreement is very good especially for 6He case. Both narrow and wide components of the distribution are reproduced very nicely. It was found[ill that the very small branch of 6He/3 decay into a and d continuum states is accounted for by a cancellation of the Gamow-Teller matrix elements between the interior and exterior halo parts and thus very sensitive to a description of the halo part. Fig. 3 compares the transition probability as a function of the a-d relative energy for the present microscopic model, the (p3/2) 2 shell model and the di-neutron cluster model, respectively. It is seen that the microscopic model gives the smaller branching ratio than the other models.
lO4
i
i
I
i
i
i
i
i
..... - - .
,
104 '7
>
10.6
10.7
Ot Experiment
~ ' ~ ' ,
10 .8
microscopic model
10.9
I
I
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
E[MeV] Figure 3. The transition probability of 6He/3 decay as a function of the a - d relative energy. Data are from Ref. [12].
Y. Suzuki et aL /Nuclear Physics A588 (1995) 15c-22c
19c
3.2. SB The ground state of SB was treated in the three-body model of a+3He+p[7]. The difference of proton and neutron radii, the skin thickness, is calculated to be 0.49 fm and is not as large as the neutron skin thickness of 6,SHe. The quadrupole moment obtained is 6.65 e fm217], which is in good agreement with the experimental value of 6.834-0.21 e fm2113]. Our calculation thus indicates that the "large" quadrupole moment[13] is naturally understood without assuming a pronounced proton halo. We conclude in agreement with Refs.[14,15] that the proton halo is not well developed in SB. Fig.4 displays the one-proton spectroscopic amplitude which is defined by an overlap integral analogous to Eq.(3). The quantity is of astrophysical interest[14]. Its Fourier transform will be tested by the momentum distribution of 7Be fragment arising from the high energy fragmentation of SB on a light target, 0.70.6-
0.5"7 S
0.4: 0.3
O)
0.2 0.1. 0 0
1
2
3
4
5
6
7
8
9 10
r (fm)
Figure 4. One-proton spectroscopic amplitude of SB.
3.3. n L i The structure of nLi is still less understood compared to other nuclei. As discussed[16, 17] in this symposium, the importance of the sl/2 orbit is stressed for the halo neutron motion. The analysis of the momentum distribution of 9Li fragment showed [18] that neither the (pl/2) 2 harmonic oscillator shell model nor the di-neutron cluster model can reproduce both narrow and wide components of the distribution. As the structure of 9Li is very well described with the a + t + n + n model[7], further study will be interesting in the six-body model of ( ~ + t + n + n + n + n where some appropriate truncations should be done for the a + t + n + n motion for 9Li. 3.4. T h e 3.563 M e V 0 + s t a t e of 6Li a n d t h e isobaric a n a l o g u e halo The nuclei near the neutron drip line have high isospin. The two-nucleon interaction in T = I channel is weaker than that in T = 0 channel and thus it is very probable that the reason why the light nuclei near the neutron drip line have halo structure is due to
20c
Y Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
their high isospin. If this is true, the halo structure is not restricted to the nuclei near the neutron drip line but may be realized in some high isospin excited states of stable nuclei as well. As the simplest example, the isobaric analogue state of nuclei with halo structure was considered[19]. The 3.563 MeV 0 + state of 6Li is an analogue state of the ground state of 6He whose halo structure is well confirmed. We ask a question of whether the state may be considered as having proton-neutron halo structure around the a-particle. As it is just 137 keV below the a + p + n threshold, a careful treatment of the Coulomb interaction is needed. A detailed calculation which allows the isospin mixing was done in the a + p + n model and has demonstrated that the proton-neutron halo naturally arises despite the isospin mixing[8]. The root mean square radius of the nucleon distribution was calculated to be 2.73 fm, even larger than that of 6He. Fig.5 compares the density distributions of 6He and 6Li and supports the isobaric analogue halo concept. The accuracy of the wave function was tested with electron scattering data.
10"2
10~
0
5
r (fm)
15
20
Figure 5. Comparison of matter density distributions of 6Li and 6He.
Encouraged by this, we Conjecture that the isospin quintuplet members (T=2, J~=0 +) of A=8 nuclei have four-nucleon halo structure around the a-particle. They include the ground states of SHe, 10.822 MeV state of SLi, 27.494 MeV state of SBe, 10.619 MeV state of SB, and the ground state of sc. As the a + n + n + n + n model is successful to get the halo structure of SHe, an analogous calculation will be done soon to inquire of the halo conjecture. As stated above the ground states (J~=2 +, T = I ) of SLi and SB are described well with the a + t + n and a+3He+p models, respectively. The isobaric analogue states of them consist of a symmetric combination of a + t + p and a+3He+n configurations. An aniti-analogue state with T--0 is an antisymmetric combination of these two. The Coulomb force may mix the isospin strongly in this case because the two channels are expected to be almost degenerate. We conjecture the two 2+ states at 16.63 and 16.92 MeV in 8Be can be understood as the states mixed in this way. The isospin thus plays an interesting role for the structure change of SBe in an a + p + p + n ÷ n model: The model
Y. Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
21c
leads to a well developed two-a cluster structure as the ground state in T = 0 channel while it will lead to 2p-2n halo structure around the a-particle in T = 2 channel.
4. SUMMARY
The microscopic multicluster model comprising such clusters as a, t, 3He, p and n was developed to describe non-uniform density distributions characteristic of the halo structure. The stochastic variational method made it possible to take full account of the complexity of the multicluster dynamics. Owing to this development a system with more than three clusters can now be solved with high accuracy. The nuclei studied with the microscopic model include ~He = a + n + n, SHe --" a + n + n + n + n, 8Li = a + t + n, 9Li = a + t + n + n, 8B = a +3 He + p, 9 C = a .[_3 He + p + p and ~Li* = a + p + n. The obtained wave functions were used to discuss the spatially extended and correlated structure of the halo part, e.g., in 6,SHe, SB and nLi. The 3.563 MeV 0 + state of 6Li was studied in detail to show that the halo structure may appear even in stable nuclei as the isospin increases. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
P.G.Hansen and B.Jonson, Europhys. Lett. 4 (1987) 409. I.Tanihata et al., Phys. Rev. Lett. 55 (1985) 276. K.Varga, Y.Suzuki and R.G.Lovas, Nucl. Phys. A571 (1994) 447. V.I.Kukulin and V.M.Krasnopol'sky, J. Phys. G3(1977)795. H.Horiuchi and Y.Kanada-En'yo, talk at this symposium. K.Varga, Y.Suzuki and Y.Ohbayasi, Phys. Rev. C50 (1994) 189. K.Varga, Y. Suzuki and I.Tanihata, to be submitted and talk at this symposium. K.Arai, Y.Suzuki and K.Varga, to be published in Phys. Rev. C. I.Tanihata et al., Phys. Lett. B289(1992)261. T.Kobayashi et al., Nucl. Phys. A538(1992)343c , Phys. Rev. Lett. 60(1988)2599. D.Baye, Y.Suzuki and P.Descouvemont, Prog. Theor. Phys. 91 (1994) 271. M.J.G.Borge et al., Nucl. Phys. A560(1993)664. T.Minamisono et al., Phys. Rev. Lett. 69(1992)2058. D.Baye, P.Descouvemont and N.K.Timofeyuk, Nucl. Phys. A577(1994)624 and talk at this symposium. H.Nakada and T.Otsuka, Phys. Rev. C49(1994)886. P.G.Hansen, talk at this symposium. W. Benenson, talk at this symposium. Y.Ogawa, Y.Suzuki and K.Yabana, Nucl. Phys. A571 (1994) 784 and talk at this symposium. Y.Suzuki and K.Yabana, Phys. Lett. B272(1991)173.
NUCLEAR PHYSICSA Nuclear Physics A588 (1995) 15c--22c
Study of hMo structure
in light nuclei with a multicluster
model
Y. Suzuki ~ * , K. Arai u , y . Ohbayasi b and K. Varga c d ~Physics Department, Niigata University, Niigata 950-21, Japan bGraduate School of Science and Technology, Niigata University, Niigata 950-21, Japan qnstitute of Nuclear Research of the Hungarian Academy of Sciences, Debrecen, P.O. Box 51, H-4001, Hungary dRIKEN, Hirosawa, Wako, Saitama 351-01, Japan Detailed structure of light exotic nuclei is described with a multicluster model comprising c~, t, aHe, p and n clusters. The multicluster dynamics is fully taken into account with the stochastic variational method. The model enables us to describe the non-uniform and spatially extended density distribution of the halo structure. It is discussed that light stable nuclei have halo-like structure as the isospin increases. 1. I N T R O D U C T I O N The neutron halo or skin structure has been disclosed near the neutron drip line of light nuclei[i,2], e.g., in the ground states of 6'SHe, mLi, m'14Be, and 17B. The halo structure is characterized by its very low density distribution extending far spatially between the core and halo parts. For a detailed description of such non-uniform halo structure a theory needs to pay attention to (i) asymptotic behavior relevant to the particle threshold and (ii) various types of correlation between the core and the halo neutrons as well as (iii) the polarizability or deformability of the core. A microscopic multicluster model has been developed[3] to describe light exotic nuclei as an aggregate of clusters such as a, t, 3He, p and n. So far the cluster model has not been used much to describe systems containing more than two clusters. However, three or more clusters must be considered for a complete description of the exotic nuclei. For example one has to go beyond the 6 H e + n + n - t y p e or a+(2n)+(2n)-type three-body models to give a realistic description of SHe. Since the dynamics of the multicluster system becomes rather complicated, we have developed a very efficient procedure to select important basis wave functions, the so-called stochastic variational method [3,4]. In contrast to the multicluster approach the mean field theory or its approximate version of the antisymmetrized molecular dynamics[5] may give an explanation for the bulk property of nuclei but has limitation in well describing individual properties of these light exotic nuclei. *Supported by a Grant-in Aid for Scientific Research (No. 05243102 and No. 06640381) of Ministry of Education , Science and Culture(Japan). 0375-9474/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved. SSDI 0375-9474(95)00093-3
Y. Suzuki et aLI Nuclear Physics A588 (1995) 15c-22c
16c
The wave functions obtained in the multicluster model calculation can be used to discuss how well we understand the halo structure. The importance of both the halo neutron correlation and the spatial extension is revealed in the analysis of the momentum distributions of the fragment in the breakup reactions of mLi and 6He, and the energy spectrum of the ~-delayed deuteron emission of 6He. To inquire of universal existence of the halo structure in nuclei other than the drip line nuclei, the structure of the 3.563 MeV 0 + state of 6Li, an analog of the 6He ground state, is investigated with the a+p+n three-body model and is shown to have density distribution spatially extended well enough to be called a proton-neutron halo around the a-particle. 2. A M I C R O S C O P I C M U L T I C L U S T E R M O D E L W I T H A S T O C H A S T I C VARIATIONAL METHOD The Hamiltonian used consists of the kinetic energy and the effective two-body internucleon potential of Minnesota type. The center-of-mass motion is properly treated. A trial wave function is built up as a sum over various cluster arrangements #, each associated with a particular set of intercluster Jacobi coordinates P f l , ' " , P~n' The wave function of the intercluster motion is described by a linear combination of nodeless harmonic oscillator functions of different size parameters: Fkt~(pP) = [ ~ - ~ - ~ T ! !
]
(p~)texp[--u~k(p~)2]Yt,,,(~),
(1)
where u~ is the kth size parameter of the ith relative motion in the cluster arrangement #. The variational trial function is thus given by
o--Z #
Z; S,(II...I,),L
"
• F"
"
,
(2)
K
where A is the intercluster antisymmetrizer which assures a fully microscopic description and Os is a vector-coupled product of the intrinsic wave function of the clusters and the spin-isospin functions and K stands for the set of the indices {kl, ..., kn} of the size parameters. The function FK(t,...l~)L is a vector-coupled product of the intercluster relative motion functions r~,,~, ( P 0 . The details can be found in Refs. [3,6-8]. The trial wave function of Eq.(2) contains a great number of terms, due riot only to the different arrangements and angular momenta but, especially, to the various size parameters. Owing to this it can describe both various types of correlation and the spatially extended halo structure. Although the use of a particular rearrangement channel in principle constitutes a complete basis, we have a number of examples which show that the energy convergence in the case is extremely slow and that the use of various rearrangement channels is superior[6]. The most efficient procedure of selecting the basis states while keeping the dimension of the basis feasible is the stochastic variational method: We generate size parameter sets by choosing randomly from an interval which corresponds to the physically important region. The parameter sets that satisfy an admittance condition are selected to be basis states. We admit a candidate if it, together with the previously selected basis states, lowers the energy more than a preset value.
Y. Suzuki et el. I Nuclear Physics A588 (1995) 15c-22c
17c
3. R E S U L T S 3.1. 6He and SHe The structure of 6He and SHe was described with the a+n+n and a + n + n + n + n models, respectively[6]. For the five-body description of SHe the following six channels were ineluded: {[(an)n]n}u, [(an)n](nn), [a(nn)](nn), {[a(nn)]n}n, {[(an)in]in}n, {[(a(nn)]n}n, The lower indices indicate that /=1 partial waves were taken in the corresponding relative motion. Most important channels of 7He+n and 6He+2n are naturally included in this model together with the possible polarizability of 6'THe. The calculated proton and neutron densities are shown in Fig. 1, confirming the thick neutron cloud.
~1°2~-
0
\ \,,~---(neu~o.)[ .~I0: iton)
,
1
2
3 r(fm)
4
5
0
1
2 3 r(fm)
4
5
Figure 1. Empirical(short-dashed curve) [9] and theoretical(solid curve) proton and neutron density of 6He and SHe. ,._., 1.6
1.6[
(a) 6He
>. 1.2
.,... 0 ' ~ 0.8
._o.o.I
/."
•
,.ID
/
~ o.4
\
I
0.0 - 200
I -100
I 0
I I00
transverse momemtum (MeV/c)
200
-200
-I00
\ 0
100
200
transeverse momemtum (MeV/c)
Figure 2. Experimental(solid curve) and theoretical(dashed curve) momentum distributions of 4He in 12C(6He,4He) reaction and 6He in 12C(SHe,6He) reaction.
18c
Y. Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
The obtained wave functions can be tested with physical observables. It is convenient to define the two-neutron spectroscopic amplitude g(r,R)
A! ) 1/2 (A--~!1!1! (kI/A-2He(~(pl--r)5(P2--R)I~A"°)"
=
(3)
As shown in Ref.[6] it can be used to calculate the momentum distribution of the fragment and the energy spectrum of the/3-delayed particle emission. Fig. 2 compares theory with experiment[10] for the momentum distributions of the 4He fragment in the (6He, 4He) reaction and of the 6He fragment in the (SHe, 6He) reaction. The agreement is very good especially for 6He case. Both narrow and wide components of the distribution are reproduced very nicely. It was found[ill that the very small branch of 6He/3 decay into a and d continuum states is accounted for by a cancellation of the Gamow-Teller matrix elements between the interior and exterior halo parts and thus very sensitive to a description of the halo part. Fig. 3 compares the transition probability as a function of the a-d relative energy for the present microscopic model, the (p3/2) 2 shell model and the di-neutron cluster model, respectively. It is seen that the microscopic model gives the smaller branching ratio than the other models.
lO4
i
i
I
i
i
i
i
i
..... - - .
,
104 '7
>
10.6
10.7
Ot Experiment
~ ' ~ ' ,
10 .8
microscopic model
10.9
I
I
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
E[MeV] Figure 3. The transition probability of 6He/3 decay as a function of the a - d relative energy. Data are from Ref. [12].
Y. Suzuki et aL /Nuclear Physics A588 (1995) 15c-22c
19c
3.2. SB The ground state of SB was treated in the three-body model of a+3He+p[7]. The difference of proton and neutron radii, the skin thickness, is calculated to be 0.49 fm and is not as large as the neutron skin thickness of 6,SHe. The quadrupole moment obtained is 6.65 e fm217], which is in good agreement with the experimental value of 6.834-0.21 e fm2113]. Our calculation thus indicates that the "large" quadrupole moment[13] is naturally understood without assuming a pronounced proton halo. We conclude in agreement with Refs.[14,15] that the proton halo is not well developed in SB. Fig.4 displays the one-proton spectroscopic amplitude which is defined by an overlap integral analogous to Eq.(3). The quantity is of astrophysical interest[14]. Its Fourier transform will be tested by the momentum distribution of 7Be fragment arising from the high energy fragmentation of SB on a light target, 0.70.6-
0.5"7 S
0.4: 0.3
O)
0.2 0.1. 0 0
1
2
3
4
5
6
7
8
9 10
r (fm)
Figure 4. One-proton spectroscopic amplitude of SB.
3.3. n L i The structure of nLi is still less understood compared to other nuclei. As discussed[16, 17] in this symposium, the importance of the sl/2 orbit is stressed for the halo neutron motion. The analysis of the momentum distribution of 9Li fragment showed [18] that neither the (pl/2) 2 harmonic oscillator shell model nor the di-neutron cluster model can reproduce both narrow and wide components of the distribution. As the structure of 9Li is very well described with the a + t + n + n model[7], further study will be interesting in the six-body model of ( ~ + t + n + n + n + n where some appropriate truncations should be done for the a + t + n + n motion for 9Li. 3.4. T h e 3.563 M e V 0 + s t a t e of 6Li a n d t h e isobaric a n a l o g u e halo The nuclei near the neutron drip line have high isospin. The two-nucleon interaction in T = I channel is weaker than that in T = 0 channel and thus it is very probable that the reason why the light nuclei near the neutron drip line have halo structure is due to
20c
Y Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
their high isospin. If this is true, the halo structure is not restricted to the nuclei near the neutron drip line but may be realized in some high isospin excited states of stable nuclei as well. As the simplest example, the isobaric analogue state of nuclei with halo structure was considered[19]. The 3.563 MeV 0 + state of 6Li is an analogue state of the ground state of 6He whose halo structure is well confirmed. We ask a question of whether the state may be considered as having proton-neutron halo structure around the a-particle. As it is just 137 keV below the a + p + n threshold, a careful treatment of the Coulomb interaction is needed. A detailed calculation which allows the isospin mixing was done in the a + p + n model and has demonstrated that the proton-neutron halo naturally arises despite the isospin mixing[8]. The root mean square radius of the nucleon distribution was calculated to be 2.73 fm, even larger than that of 6He. Fig.5 compares the density distributions of 6He and 6Li and supports the isobaric analogue halo concept. The accuracy of the wave function was tested with electron scattering data.
10"2
10~
0
5
r (fm)
15
20
Figure 5. Comparison of matter density distributions of 6Li and 6He.
Encouraged by this, we Conjecture that the isospin quintuplet members (T=2, J~=0 +) of A=8 nuclei have four-nucleon halo structure around the a-particle. They include the ground states of SHe, 10.822 MeV state of SLi, 27.494 MeV state of SBe, 10.619 MeV state of SB, and the ground state of sc. As the a + n + n + n + n model is successful to get the halo structure of SHe, an analogous calculation will be done soon to inquire of the halo conjecture. As stated above the ground states (J~=2 +, T = I ) of SLi and SB are described well with the a + t + n and a+3He+p models, respectively. The isobaric analogue states of them consist of a symmetric combination of a + t + p and a+3He+n configurations. An aniti-analogue state with T--0 is an antisymmetric combination of these two. The Coulomb force may mix the isospin strongly in this case because the two channels are expected to be almost degenerate. We conjecture the two 2+ states at 16.63 and 16.92 MeV in 8Be can be understood as the states mixed in this way. The isospin thus plays an interesting role for the structure change of SBe in an a + p + p + n ÷ n model: The model
Y. Suzuki et al. / Nuclear Physics A588 (1995) 15c-22c
21c
leads to a well developed two-a cluster structure as the ground state in T = 0 channel while it will lead to 2p-2n halo structure around the a-particle in T = 2 channel.
4. SUMMARY
The microscopic multicluster model comprising such clusters as a, t, 3He, p and n was developed to describe non-uniform density distributions characteristic of the halo structure. The stochastic variational method made it possible to take full account of the complexity of the multicluster dynamics. Owing to this development a system with more than three clusters can now be solved with high accuracy. The nuclei studied with the microscopic model include ~He = a + n + n, SHe --" a + n + n + n + n, 8Li = a + t + n, 9Li = a + t + n + n, 8B = a +3 He + p, 9 C = a .[_3 He + p + p and ~Li* = a + p + n. The obtained wave functions were used to discuss the spatially extended and correlated structure of the halo part, e.g., in 6,SHe, SB and nLi. The 3.563 MeV 0 + state of 6Li was studied in detail to show that the halo structure may appear even in stable nuclei as the isospin increases. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
P.G.Hansen and B.Jonson, Europhys. Lett. 4 (1987) 409. I.Tanihata et al., Phys. Rev. Lett. 55 (1985) 276. K.Varga, Y.Suzuki and R.G.Lovas, Nucl. Phys. A571 (1994) 447. V.I.Kukulin and V.M.Krasnopol'sky, J. Phys. G3(1977)795. H.Horiuchi and Y.Kanada-En'yo, talk at this symposium. K.Varga, Y.Suzuki and Y.Ohbayasi, Phys. Rev. C50 (1994) 189. K.Varga, Y. Suzuki and I.Tanihata, to be submitted and talk at this symposium. K.Arai, Y.Suzuki and K.Varga, to be published in Phys. Rev. C. I.Tanihata et al., Phys. Lett. B289(1992)261. T.Kobayashi et al., Nucl. Phys. A538(1992)343c , Phys. Rev. Lett. 60(1988)2599. D.Baye, Y.Suzuki and P.Descouvemont, Prog. Theor. Phys. 91 (1994) 271. M.J.G.Borge et al., Nucl. Phys. A560(1993)664. T.Minamisono et al., Phys. Rev. Lett. 69(1992)2058. D.Baye, P.Descouvemont and N.K.Timofeyuk, Nucl. Phys. A577(1994)624 and talk at this symposium. H.Nakada and T.Otsuka, Phys. Rev. C49(1994)886. P.G.Hansen, talk at this symposium. W. Benenson, talk at this symposium. Y.Ogawa, Y.Suzuki and K.Yabana, Nucl. Phys. A571 (1994) 784 and talk at this symposium. Y.Suzuki and K.Yabana, Phys. Lett. B272(1991)173.