Halo nuclei are among the strangest nuclear structures. They are viewed as a core containing most of the nucleons surrounded by one or two loosely bound nucleons. These have a high probability of presence at a large distance from the core. Therefore, they constitute a sort of halo surrounding the other nucleons. The core, remaining almost unperturbed by the presence of the halo is seen as a usual nucleus. <P> The Coulomb breakup reaction is one of the most useful tools to study these nuclei. It corresponds to the dissociation of the halo from the core during a collision with a heavy (high <I>Z</I>) target. In order to correctly extract information about the structure of these nuclei from experimental cross sections, an accurate theoretical description of this mechanism is necessary. <P> In this work, we present a theoretical method for studying the Coulomb breakup of one-nucleon halo nuclei. This method is based on a semiclassical approximation in which the projectile is assumed to follow a classical trajectory. In this approximation, the projectile is seen as evolving in a time-varying potential simulating its interaction with the target. This leads to the resolution of a time-dependent Schrödinger equation for the projectile wave function. <P> In our method, the halo nucleus is described with a two-body structure: a pointlike nucleon linked to a pointlike core. In the present state of our model, the interaction between the two clusters is modelled by a local potential. <P> The main idea of our method is to expand the projectile wave function on a three-dimensional spherical mesh. With this mesh, the representation of the time-dependent potential is fully diagonal. Furthermore, it leads to a simple representation of the Hamiltonian modelling the halo nucleus. This expansion is used to derive an accurate evolution algorithm. <P> With this method, we study the Coulomb breakup of three nuclei: ¹¹Be, ¹⁵C and ⁸B. ¹¹Be is the best known one-neutron halo nucleus. Its Coulomb breakup has been extensively studied both experimentally and theoretically. Nevertheless, some uncertainty remains about its structure. The good agreement between our calculations and recent experimental data suggests that it can be seen as a <I>s1/2</I> neutron loosely bound to a ¹⁰Be core in its 0⁺ ground state. However, the extraction of the corresponding spectroscopic factor have to wait for the publication of these data. <P> ¹⁵C is a candidate one-neutron halo nucleus whose Coulomb breakup has just been studied experimentally. The results of our model are in good agreement with the preliminary experimental data. It seems therefore that ¹⁵C can be seen as a ¹⁴C core in its 0⁺ ground state surrounded by a <I>s1/2</I> neutron. Our analysis suggests that the spectroscopic factor corresponding to this configuration should be slightly lower than unity. <P> We have also used our method to study the Coulomb breakup of the candidate one-proton halo nucleus ⁸B. Unfortunately, no quantitative agreement could be obtained between our results and the experimental data. This is mainly due to an inaccuracy in the treatment of the results of our calculations. Accordingly, no conclusion can be drawn about the pertinence of the two-body model of ⁸B before an accurate reanalysis of these results. <P> In the future, we plan to improve our method in two ways. The first concerns the modelling of the halo nuclei. It would be indeed of particular interest to test other models of halo nuclei than the simple two-body structure used up to now. The second is the extension of this semiclassical model to two-neutron halo nuclei. However, this cannot be achieved without improving significantly the time-evolution algorithm so as to reach affordable computational times.

Halo nuclei are among the strangest nuclear structures.<p>They are viewed as a core containing most of the nucleons<p>surrounded by one or two loosely bound nucleons. <p>These have a high probability of presence at a large distance<p>from the core.<p>Therefore, they constitute a sort of halo surrounding the other nucleons.<p>The core, remaining almost unperturbed by the presence<p>of the halo is seen as a usual nucleus.<p><p><P><p><p>The Coulomb breakup reaction is one of the most useful<p>tools to study these nuclei. It corresponds to the<p>dissociation of the halo from the core during a collision<p>with a heavy (high <I>Z</I>) target.<p>In order to correctly extract information about the structure of<p>these nuclei from experimental cross sections, an accurate<p>theoretical description of this mechanism is necessary.<p><p><P><p><p>In this work, we present a theoretical method<p>for studying the Coulomb breakup of one-nucleon halo nuclei.<p>This method is based on a semiclassical approximation<p>in which the projectile is assumed to follow a classical trajectory.<p>In this approximation, the projectile is seen as evolving<p>in a time-varying potential simulating its interaction with the target.<p>This leads to the resolution of a time-dependent Schrödinger<p>equation for the projectile wave function.<p><p><P><p><p>In our method, the halo nucleus is described<p>with a two-body structure: a pointlike nucleon linked to a<p>pointlike core.<p>In the present state of our model, the interaction between<p>the two clusters is modelled by a local potential.<p><p><P><p><p>The main idea of our method is to expand the projectile wave function<p>on a three-dimensional spherical mesh.<p>With this mesh, the representation of the time-dependent potential<p>is fully diagonal.<p>Furthermore, it leads to a simple<p>representation of the Hamiltonian modelling the halo nucleus.<p>This expansion is used to derive an accurate evolution algorithm.<p><p><P><p><p>With this method, we study the Coulomb breakup<p>of three nuclei: ¹¹Be, ¹⁵C and ⁸B.<p>¹¹Be is the best known one-neutron halo nucleus.<p>Its Coulomb breakup has been extensively studied both experimentally<p>and theoretically.<p>Nevertheless, some uncertainty remains about its structure.<p>The good agreement between our calculations and recent<p>experimental data suggests that it can be seen as a<p><I>s1/2</I> neutron loosely bound to a ¹⁰Be core in its<p>0⁺ ground state.<p>However, the extraction of the corresponding spectroscopic factor<p>have to wait for the publication of these data.<p><p><P><p><p>¹⁵C is a candidate one-neutron halo nucleus<p>whose Coulomb breakup has just been studied experimentally.<p>The results of our model are in good agreement with<p>the preliminary experimental data. It seems therefore that<p>¹⁵C can be seen as a ¹⁴C core in its 0⁺<p>ground state surrounded by a <I>s1/2</I> neutron.<p>Our analysis suggests that the spectroscopic factor<p>corresponding to this configuration should be slightly lower<p>than unity.<p><p><P><p><p>We have also used our method to study the Coulomb breakup<p>of the candidate one-proton halo nucleus ⁸B.<p>Unfortunately, no quantitative agreement could be obtained<p>between our results and the experimental data.<p>This is mainly due to an inaccuracy in the treatment<p>of the results of our calculations.<p>Accordingly, no conclusion can be drawn about the pertinence<p>of the two-body model of ⁸B before an accurate reanalysis of these<p>results.<p><p><P><p><p>In the future, we plan to improve our method in two ways.<p>The first concerns the modelling of the halo nuclei.<p>It would be indeed of particular interest to test<p>other models of halo nuclei than the simple two-body structure<p>used up to now.<p>The second is the extension of this semiclassical model to<p>two-neutron halo nuclei.<p>However, this cannot be achieved<p>without improving significantly the time-evolution algorithm so as to<p>reach affordable computational times. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished