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A Doorway to Borromean Halo Nuclei: the Samba Configuration

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A Doorway to Borromean Halo Nuclei: the Samba Configuration A doorway to Borromean halo nuclei: the Samba configuration M. T. Yamashita Universidade Estadual Paulista, CEP 18409-010 Itapeva, SP, Brasil T. Frederico Departamento de F´ısica, Instituto Tecnol´ogico de Aeron´autica, Centro T´ecnico Aeroespacial, 12228-900 S˜ao Jos´edos Campos, Brasil M. S. Hussein Instituto de F´ısica, Universidade de S˜ao Paulo, C.P. 66318, CEP 05315-970 S˜ao Paulo, Brasil (Dated: October 22, 2018) We exploit the possibility of new configurations in three-body halo nuclei - Samba type - (the neutron-core form a bound system) as a doorway to Borromean systems. The nuclei 12Be, 15B, 23N and 27F are of such nature, in particular 23N with a half-life of 37.7 s and a halo radius of 6.07 fm is an excellent example of Samba-halo configuration. The fusion below the barrier of the Samba halo nuclei with heavy targets could reveal the so far elusive enhancement and a dominance of one-neutron over two-neutron transfers, in contrast to what was found recently for the Borromean halo nucleus 6He + 238U. PACS numbers: 25.70.Jj, 25.70.Mn, 24.10.Eq, 21.60.-n Borromean nuclei, be them halo or not, are quite com- isotope exists in oxygen (see, however, Ref. [1]). mon and their study has been intensive [1, 2, 3, 4]. These As an example we consider the boron isotopes: A = three-body systems have the property that any one of 8, 9, 10, 11, 12, 13, 14, 15, 17, 19. Both 17B and 19B their two-body subsystems is unbound. The halo-type would be Borromean halo nuclei (19B more so). The Borromean nuclei are of special interest as they are unsta- isotope 15B is the doorway configuration. The halo ra- ble and their radii are quite large compared to neighbor- dius is 5.15 fm while nuclear radius is 2.91 fm, to be 11 6 ing stable nuclei. Typical cases are Li [5] and He [6]. compared to 2.50 fm of normal A = 15 nucleus. The de- 4 9 The cores, c, He and Li are bound but the three two- tails of our radius calculation are given below. We have 5 10 body subsystems are not; He and Li and the nn sys- identified five candidates for Samba halo nuclei [7, 8] of tem (n represents a neutron). Borromean excited states the doorway type. They are 12Be, 15B, 20C, 23N and of stable nuclei also exist. A well known example is the 27F. The name Samba partly is inspired by the work of 12 Hoyle resonance in C at an excitation energy of about Robicheaux [9] who exploited yet another type of halo 6.8 MeV. This resonance, of paramount importance in three-body systems, such as the hypertriton 3 H , where 4 Λ 1 stellar nucleo-synthesis, is a cluster of three He nuclei, only one of the two-body subsystems is tightly bound, 8 with the unbound Be as two-body subsystems. and called such systems Tango halo systems. Whereas, An important issue that has to be addressed is how the the Tango halo nucleus has a bound two-body subsys- halo Borromean nuclei are formed as more neutrons are tem that has to move in a rather “harmonic” fashion in added to a given stable nucleus. In order to answer this the presence of the core, the Samba nucleus (two of the arXiv:nucl-th/0501052v3 17 Feb 2006 question we have made a survey of the isotopes of several two-body subsystems are tightly bound) is distinguished nuclei in the proton p-shell region as well as the fluorine by the fact that the motion of the two-neutron subsys- isotopes. We have discovered that the halo develops in tem can be a rather more “agitated” and the three-body the Borromean nuclei in a gradual fashion. Further, to system remains bound. reach the halo Borromean nucleus the system, two neu- We have calculated the reduced dipole transition trons down, acquires a new configuration which in several strengths B(E1) and the radii of these five candidates for cases is a halo-type as well. This new type of halo nuclei Samba halo nuclei. The B(E1)’s were calculated using has the feature that only one of its two-body subsystems, a simple cluster model usually employed to get a rough the di-neutron, is unbound. The other two subsystems estimate [10]. This model treats the two neutrons as a are weakly bound. Another feature of this configuration cluster that vibrates against the core. A Yukawa type is that the one neutron separation energy, En, is smaller wave function is used to describe the ground state and than that of the two-neutron, E2n, in contrast to the a plane wave is employed for the final continuum state Borromean halo nuclei where En > E2n. Of course the in the calculation of the dipole matrix element. The situation En < E2n that prevails in the new “doorway” model allows for the derivation of a simple analytical for- configuration is shared by the other normal isotopes. In mula for the dipole strength distribution, dB(E1)/dE∗. what follows we shall use the available information about The dipole distribution is an important quantity in the the isotopes studied here contained in the Nuclear Wal- study of exotic nuclei that is usually measured through let Cards (Sixth edition, 2000). Note that no Borromean the electromagnetic dissociation of these fragile systems 2 in the field of a heavy target such as 208Pb. Integrating 1.6 ∗ ∗ dB(E1)/dE over E gives the B(E1) value. The cluster circles - Be model gives a simple formula for this squares - B triangles - C 3e2 2Z 2 1 B(E1) = , (1) diamond - N 16πµ A E2n 1.4 stars - F where µ is the reduced mass of the core and the 2n clus- ter. The factor 2Z/A corresponds to the number of neu- 0 trons in the halo, 2; the charge of the core, Z and the R/R mass number of the whole halo nucleus, A. Note that 1.2 the two neutron separation energy is inversely propor- tional to the average distance between the core center 2 and the three-body center-of-mass (CM), hrc−CM i, which is used as the healing distance of the clusterq model 12 wave function. For, e.g., Be we find for B(E1) the 1.0 value 0.043 e2fm2 (another calculation gives 0.05-0.06 2 3 4 5 6 2 2 2 2 e fm [11]) to be compared with 0.051(13) e fm for the T experimental value [12] and to 0.61 e2fm2 for the well Z developed halo in the Borromean nucleus 6He. Thus one should be able to get reasonably reliable and apprecia- FIG. 1: Halo radii of our candidates for two-neutron halo ble dissociation cross section for this Samba nucleus (the nuclei in isotopes indicated in the legend. The full symbols are the Samba type nuclei (results from Table I) and the open yield or production cross section of these nuclei should symbols are the Borromean nuclei. All the points are divided be larger than those of the Borromean halo nuclei [14], by the the isotope radii, R0, calculated assuming a normal rendering the experiment quite feasible). It is worth men- nature of the isotope. Tz is the isospin projection. tioning here that for Tango halo nuclei, where the halo is a pair of proton-neutron, the B(E1) is similar to Eq. (1) except for the energy E2n, which is replaced by Epn and the factor (2Z/A)2 which is replaced by [(A − 2Z)/A]2. Conspicuous in the figure is lack of indication of one- This will render the B(E1) for Tango halo nuclei a fac- neutron halo nuclei whose radii are quite large and de- 2 11 19 tor [(A − 2Z)/2Z] smaller than that of a corresponding viant from R0. These nuclei, such as Be, C and others Samba or Borromean nucleus if E2n is maintained equal have been shown to have a well developed one-neutron to Epn. halo. We did not show these halo nuclei as the thrust In figure (1) we show the halo radii of our candidates of our work here is on three-body, two-neutron halo nu- for two-neutron halo nuclei as a function of the isospin clei. Also absent in the figure is the, what would be, projection Tz = (N − Z)/2. These radii can be esti- Borromean halo nucleus following the Samba one, 23N. mated from the neutron-CM root mean square radius We are tempted to predict that such a nucleus, 25N, may h¯2 2 exist, though we have no information about En, E2n and hrn−CM i estimated as ρ mnS3 (see Refs. [7] and [8]). q q its life time. From the above considerations and we can The quantity rho is adimensional. For our purposes ρ is 20 obtained calculating the average (R(14Be)+ R(17B))/2 clearly rule out C as a Samba halo nucleus and accord- ingly 22C as a Borromean halo nucleus. 2 and associating this to squareroot hrn−CM i above. 14 17 q The “doorway” aspect of the Samba halo nuclei is quite Here R( Be)=3.74 fm and R( B)=3.8 fm, from evident especially in the circles, squares and stars. They Ref. [2], S3 is the three-body energy with respect to the always precedes the final Borromean halo nucleus in the binding energy of the neutron in the two-body subsys- chain of isotopes.
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