Physics with loosely bound nuclei

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—journal of Aug. & Sept. 2001

physics pp. 519–524

Physics with loosely bound nuclei

CHHANDA SAMANTA

Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India Physics Department, Virginia Commonwealth University, Richmond, VA 23284, USA

Abstract. The essential aspect of contemporary physics is to understand properties of nucleonic matter that constitutes the world around us. Over the years research in nuclear physics has provided strong guidance in understanding the basic principles of nuclear interactions. But, the scenario of nuclear physics changed drastically as the new generation of accelerators started providing more and more rare isotopes, which are away from the line of stability. These weakly bound nuclei are found to exhibit new forms of nuclear matter and unprecedented exotic behaviour. The low breakup thresholds of these rare nuclei are posing new challenges to both theory and experiments. Fortunately, nature has provided a few loosely bound stable nuclei that have been studied thoroughly for decades.

Attempts are being made to find a consistent picture for the unstable nuclei starting from their stable counterparts. Some significant differences in the structure and reaction mechanisms are found.

Keywords. Stable and unstable Li and He; halo; skin; soft dipole resonance.

PACS Nos 25.80.Ls; 21.10.Gv; 21.60.Gx; 24.30.Go; 27.20.+n

In last few decades, with the advent of more and more powerful accelerators, the world has witnessed an explosion of information on nuclei and it has created considerable influence on our day to day life. Nevertheless, complete understanding of the fundamental nucleon–

nucleon interaction has not been achieved yet. Exactly when it was felt that nuclear physics has possibly reached its saturation, a drastic change in scenario occurred in 1985 with the discovery of a loosely bound isotope of lithium, called¹¹Li. Lithium has two stable isotopes,⁶Li and⁷Li. With the addition of extra neutrons, the neutron-rich isotopes of Li go away from the line of stability and, finally reach the neutron drip line where the one- neutron separation energy^(Sn

)becomes zero. While most of the proton drip line^(Sp

=0)

nuclei have been found, the neutron drip line has been reached for low^Znuclei only. The nuclei near the drip lines are found to delineate many properties that can not be explained by the conventional nuclear physics.

The first surprising deviation from the conventional nuclear physics was noticed through measurement of the interaction cross section, which led to the discovery of the anomalously large radius of the¹¹Li nucleus and its exotic shape, called ‘halo’ [1]. Since then, several such nuclei have been discovered with exotic shape, size and internal structure. While the ¹¹Li nucleus has a ⁹Li-core plus two neutron-halo, the ¹¹Be has only one neutron halo. Recently, in¹²Be, a very elongated ‘dimmer’ configuration has been found at higher excitation energies. Another important discovery is the neutron-skin formation in the ⁶He nucleus although it has only a few nucleons [2]. Such a skin was not found even in the

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Chhanda Samanta

208Pb nucleus that has large neutron–proton asymmetry. Most interesting finding is the existence of the bound³¹F nucleus [3], which is beyond the neutron drip line prescribed by the well known Bethe–Weizs¨acker mass formula. The internal structure of such loosely bound nuclei is found to deviate from the conventional spherical shell structure, a known characteristic of nuclei close to the line of stability. For example, this can be seen in ¹¹Be for which the ground state spin parity is¹⁼²⁺instead of¹⁼² indicating lowering of the

2s

1=2state below^1p1=2[4].

Such exotic phenomena have given birth to many new ideas. It was predicted that thin and extended neutron distribution might lead to a new kind of collective motion in halo nuclei [5] in which the outer halo neutrons move against the remaining core nucleus. As the frequencies of these kinds of collective modes are expected to be low compared to the collective motions of all neutrons–protons in general, they are called soft dipole resonance (SDR) modes, in contrast to the well-known giant dipole resonance (GDR) mode. Since the existence of such an exotic mode would be a definite signature of the halo structure of the ground state, experimental searches for this mode have been made through various reactions, such as¹¹Li^!⁹Li⁺2ⁿCoulomb dissociation [6], pion double exchange

11B( ,⁺)¹¹Li reactions [7], the pion capture reaction¹⁴C⁽ ^;^pd)¹¹Li [8], and proton scattering¹¹Li^(p;^p⁰⁾¹¹Lireactions [9]. In high resolution experiments at RIKEN [9], it was possible to identify several excited states of¹¹Li through precise measurements of^p+

11Li scattering in inverse kinematics atÊ(¹¹Li)⁼75Âand 68ÂMeV. A large breakup cross section was seen above the¹¹Li^!⁹Li⁺²ⁿbreakup threshold (0.3 MeV). A sharp peak at 1.3 MeV was found, the position of which did not change with the detection angles. It was identified as the resonant excited state of¹¹Li and its angular distribution was measured.

Karataglidis et al [10] questioned the existence of this 1.3 MeV resonance as an excited state of¹¹Li. They performed shell-model calculations, which produced a reasonable fit to the elastic scattering data. However, their single-particle excitation picture failed to explain the inelastic angular distribution. To account for the discrepancy they proposed a ‘shakeoff’ model. In the ‘shakeoff’ mechanism, a quasifree (QF) scattering between a proton and the⁹Li core of the¹¹Li nucleus takes place. Calculations in this model, scaled by a factor of 0.5, is close to the experimental angular distribution data profile of the 1.3 MeV excited state. But, with changing detection angles, the position of the QF peak is expected to move with respect to the elastic peak whereas, for a real excited state, the energy difference between the elastic and the peak under discussion would remain fixed at all angles. The latter was found to be true in the actual experiment. In addition, observation of a resonance around 1 MeV in the pion capture reaction is a supportive evidence of the existence of the excited state. A resonance due to the ‘shakeoff’ mechanism cannot appear in such pion induced reactions. In a microscopic framework we showed (figure 1) that this low-lying dipole resonance in¹¹Li arises due to a collective oscillation between the core and the halo neutrons giving rise to an ‘isovector’ SDR mode [11,12].

The controversy on the existence of the resonance state at 1.3 MeV mainly arose as the

11Li^!⁹Li⁺²ⁿbreakup data of MSU [13] could be explained by the direct breakup of

11Li into three-body continuum, without assumption of a resonance. The fragments from the energetic projectile breakup, measured in coincidence, can pinpoint whether the reaction mechanism was direct or sequential. Sequential decay occurs when there is a definite resonance excited state. From a measurement of the low energy (6–8^AMeV) ^6;7Li projectile breakup we showed that if the measurement is done beyond the grazing angle, it

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Figure 1. (a): The¹¹Li^(p;^p)¹¹Li elastic angular distribution at^E ⁼^68AMeV and predictions of one step DWBA calculations. The solid (dashed) line indicates results with(without) the spin-orbit interaction parameters. (b) The¹¹Li^(p;^p⁰⁾¹¹Li (1.3 MeV) inelastic angular distribution at^E⁼^68AMeV and one-step DWBA predictions.

The dotted line indicates predictions with the spin-orbit parameters omitted in the exit channel only.

becomes much easier to identify the sequential breakup [14]. In a wide-angle measurement it was shown that the direct breakup part dies out with the increase of scattering angle where the sequential contributions remain significant. While¹¹Li is known to be a halo nucleus with two neutrons around a⁹Li core, the neutrons in⁶He and⁸He were predicted to form skin around their respective⁴He core. Both nuclei have low breakup thresholds. To understand the structure and reaction dynamics of these nuclei, a consistent analysis of the available low energy (25–75A MeV) proton elastic scattering data on^4;6;8He and^6;7;9;11Li

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Chhanda Samanta

Figure 2. The experimental angular distribution and folding model analysis (employing SBM interaction) of proton-elastic scattering with (a)⁴He at^31AMeV,⁶He at^25:2A MeV and⁸He at^32AMeV, (b)⁴He at^40AMeV and⁶He at^41:6AMeV, (c)⁴He at

72AMeV,⁶He at^71AMeV and⁸He at^72:5AMeV, (d)⁶Li at ^25:9, ^40:1, ⁶⁵and

72AMeV, (e)⁷Li at⁶⁵,^67:8AMeV and¹¹Li at^68:4AMeV, (f)⁴He at^72AMeV,⁹Li at^60AMeV and¹¹Li at⁶²and^75AMeV. For the⁶He nucleus only the calculations employing the Q1 model density are shown.

nuclei was carried out [15] in a folding model framework. A finite-range, momentum, density and isospin dependent^NN interaction (SBM) was folded with realistic densities of different nuclei. To fit the elastic angular distribution (figure 2), the real part of the folded potentials were multiplied by a renormalization factor^(NR

). Except for the^p ⁺ ⁴He scattering at low incident energy, the^NRvalues were found to be significantly different

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Figure 3. Predictions of the angular distributions of the⁶He^(p;^p⁰⁾⁶He(1.8 MeV) and the⁶He^(p;^p⁰⁾⁶He(4.0 MeV) inelastic scatterings at^25:2AMeV showing negligible effects of the different density prescriptions and different^NR^F^F:

from 1.0, indicating appreciable channel coupling effects in the energy region considered.

Variation of^NRvalues with incident energies for⁶He and¹¹Li is much smaller compared to that of⁸He and⁶Li. This indicates that reaction dynamics of⁶He and⁸He are different.

The^NRvalues of⁶He and¹¹Li do not approach the value^NR

=1:0in the said energy range. This possibly occurs as the ground states of⁶He and¹¹Li nuclei are very close to the continuum that induces large coupling irrespective of incident energies. This is an important finding in the context of Coulomb dissociation studies for which one-step reaction mechanism (i.e.,^NR

=1:0) is essential to extract astrophysical information from the projectile breakup data.

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Chhanda Samanta

Further analysis of proton inelastic scattering data on these nuclei demonstrates that renormalizations of the real part of the form factors are needed to fit the experimental data of⁷Li ^(p;^p⁰⁾⁷Li (^0:478MeV) at^E ⁼ ^49:75AMeV,¹¹Li^(p;^p⁰⁾¹¹Li (1.3 MeV) at

E=68:4AMeV,⁸He^(p;^p⁰⁾⁸He(3.57 MeV) at^E⁼^72:5AMeV. Analysis on the same footing enabled us to make predictions for the unknown angular distributions of the^p+

6He inelastic scattering at^E⁼^25:2AMeV leading to the 1.8 MeV^(L⁼²⁾and 4.0 MeV

(L=1)excited states (figure 3).

Inclusion of various different ground state density distributions (P1, Q1, C) of varying r.m.s radii (2.32 fm to 2.76 fm) [15] was found to cause no appreciable difference in the said predictions [16]. The journey from the stable to the unstable isotopes of Li and He thus reveals interesting change in their structure and reaction dynamics. There are still many more nuclei for which such comparison is needed. Although most of the proton drip nuclei have been found, the very neutron drip line nuclei are not yet reached. This is mainly due to limitations of the present accelerator facilities. However, in near future, several upcoming/proposed facilities (NSCL, MSU; RIBF, RIKEN; SPIRAL, GANIL; RIA, USA etc.) are expected to provide a large number of neutron/proton-rich nuclei. Nuclear physics is poised to encounter a great advancement.

References

[1] I Tanihata, J. Phys. G22, 157 (1996)

[2] A A Korsheninnikov et al, Nucl. Phys. A617, 45 (1997) [3] H Sakurai et al, Phys. Lett. B448, 180 (1999)

[4] M Fukuda et al, Phys. Lett. B268, 339 (1991)

[5] P G Hansen and B Jonson, Europhys. Lett. 4, 409 (1987) K Ikeda, Nucl. Phys. A538, 355c (1992)

[6] T Kobayashi et al, Phys. Lett. B232, 51 (1989) [7] T Kobayashi et al, Nucl. Phys. A538, 343c (1992) [8] M G Gornov et al, Phys. Rev. Lett. 81, 4325 (1998) [9] A A Korsheninnikov et al, Phys. Rev. Lett. 78, 2317 (1997) [10] S Karataglidis et al, Phys. Rev. Lett. 79, 1447 (1997) [11] R Kanungo and C Samanta, J. Phys. G24, 1611 (1998)

[12] R Kanungo, I Tanihata and C Samanta, Prog. Theor. Phys. 102, 1133 (1999) [13] D Sackett et al, Phys. Rev. C48, 118 (1993)

[14] D Gupta et al, Nucl. Phys. A646, 161 (1999) [15] D Gupta et al, Nucl. Phys. A674, 77 (2000) [16] D Gupta et al, (to be communicated)