(d, P) Reaction To Determine The Unstable Nuclei Astrophysics (p, Gamma) Reaction Rate

The proton capture reactions on proton-rich nuclei play an important rolein explosive hydrogen burning in the peculiar astrophysical sites where the tem-perature and density are so high that the capture reactions become faster thanthe competingβdecays. Determination of the cross sections of these astrophys-ical reactions is a major challenge for nuclear physics and nuclear astrophysics.Direct measurement of cross sections is the most exact, however, many of thesereactions are difficult to measure directly with currently available experimentaltechniques because the cross sections at low energies are very small (nb-pb) andthe available intensities of the radioactive ion beams are very low. It is thereforeimportant to explore indirect alternative methods for determining the (p,γ) re-action cross sections on unstable nuclei.Recently, the proton transfer reactions and ANC approach have been exten-sively applied to the study of radiative capture reactions. In this method, theANC of virtual decay can be derived from proton transfer reactions with largecross sections (mb), and then used to calculate the astrophysical S factors andrates of direct captures in radiative capture reactions.In this thesis, I used the ANC method combined with charge symmetry ofmirror nuclei which is a little bit different from traditional ANC approach. Mir-ror nuclei include a pair of nuclei that have the same mass number. If the proton-and neutron numbers are interchanged in the one of mirror pair, this nucleus willbe transformed into the other. The corresponding levels of mirror pair are ana-logical due to charge symmetry of strong interaction. Assume B and D are mirrornuclei, then some of the information of D nucleus can be found by studying Bnucleus. In order to study the C(p,γ)D reaction, the proton transfer reactionsuch as C(d, n)D needs to be measured in traditional ANC approach. The pro-ton ANC of D virtual decay can be then extracted and employed to computethe astrophysical S factors and rates of direct captures in the C(p,γ)D reaction.While the neutron transfer reaction such as A(d,p)B will be measured in the ANC method combined with charge symmetry of mirror nuclei. The neutronANCs of B virtual decays can be derived through DWBA analysis. The protonANC of D virtual decay can be then extracted according to charge symmetryand utilized to calculate the astrophysical S factors and rates of the C(p,γ)Dreaction.It should be mentioned that both the direct capture contribution and protonwidths of resonant captures can be obtained by using this method.This method has two advantages. (1) The preexisting radioactive beamsproduced by GIRAFFE can be used to study new radiative capture reactionsbesides those studied by traditional ANC approach. (2) The experimentally un-known cross sections of radiative capture reaction may be indirectly determined,or the statistical uncertainty of cross sections can be significantly reduced throughthis method. The ⁸B(p,γ)⁹C and ²⁶Si(p,γ)²⁷P reactions are just the examples ofthese two advantages. In order to study ⁸B(p,γ)⁹C, the ⁸B beam is needed intraditional ANC approach, which has not been produced yet by GIRAFFE. How-ever, the ⁸Li beam is available at GIRAFFE. Thus, one can measure the angulardistribution of ⁸Li(d, p)⁹Li, and then indirectly study the ⁸B(p,γ)⁹C reaction bythe ANC method combined with charge symmetry. In addition, the angulardistributions of ²⁶Mg(d,p)²⁷Mg can be applied to the study of the ²⁶Si(p,γ)²⁷Preaction by this method. Because the intensity of stable deuteron beam is sig-nificantly larger than that of unstable ²⁶Si beam, the statistics will be largelyimproved. The contribution from direct capture in the ²⁶Si(p,γ)²⁷P reaction hasbeen determined experimentally in the present work, for the first time.The ANC method is an indirect experimental approach, therefore, its re-liability is rather concerned. In this thesis, I have derived the astrophysical Sfactors of the ¹⁶O(p,γ)¹⁷F reaction leading to the ground and first excited statesof ¹⁷F from the angular distributions of the ¹⁶O(d,p)¹⁷O reaction leading to theground and first excited states of ¹⁷O using the ANC method combined withcharge symmetry. The present S factors have been compared with those fromthe direct measurement experiment. It shows that the results by ANC methodare in good agreement with those from the direct measurement at astrophysicalenergies within the uncertainties. Therefore, the results from ANC method can provide an experimental constraint to the cross sections and rates of radiativecapture reactions in the case that the data from direct measurement are notavailable. In addition, the data at very low energies from the extrapolation ofdirect results at higher energies can be checked by those from ANC method.In this dissertation, the ANC method combined with charge symmetry isutilized to study four reactions of importance in hydrogen burning, namely⁸B(p,γ)⁹C, ¹¹C(p,γ)¹²N, ¹³N(p,γ)¹⁴O and ²⁶Si(p,γ)²⁷P. In addition, this methodcan be applied to the study of many other reactions of astrophysical importance,for example, ⁷Be(p,γ)⁸B, ¹⁷F(p,γ)¹⁸Ne, ²²Mg(p,γ)²³Al and so on.In addition, two more experiments are presented in this thesis. The firstone is the production of intense radioactive beams using low energy protons atTRIUMF lab; the second one is the measurement of the ¹³N(d, n)¹⁴O angular dis-tribution at GIRAFFE facility of CIAE and the indirect study of the ¹³N(p,γ)¹⁴Oreaction.The outline of this thesis is as follows. Chapter 1 will briefly introduce nu-clear astrophysics and hydrogen burning in evolution of stars. Chapter 2 willpresent the thermonuclear reaction formalism and experimental methods. Chap-ter 3 is the principal part of this thesis, where the ANC method combined withcharge symmetry of mirror nuclei will be introduced and tested for its reliability,and then used to study four important reactions in hydrogen burning. Chapter 4will present two other works during my PHD course. Chapter 5 has a summaryof this dissertation and a discussion on ANC method.