MAY EXAMINATIONS 2013
PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 MAY EXAMINATIONS 2013 Master of Mathematics: Year 4 Master of Physics: Year 4 ADVANCED NUCLEAR PHYSICS TIME ALLOWED: 1 hour and a half INSTRUCTIONS TO CANDIDATES Answer all questions. Question 1 and 2 each carry 50% of the total marks. Answer either part (a) or part (b) of question 2. In the event of a student answering both parts of an either/or question and not clearly crossing out one answer, only the answer to part (a) of the question will be marked. The marks allotted to each part of a question are indicated in square brackets. All symbols have their usual meanings unless otherwise stated. PAPER CODE PHYS490 Page 1 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 1. Answer all questions [a] Assuming the charge independence of the nuclear force, explain why there is no bound state for the two-neutron or two-proton systems while a neutron and a proton can form a [b] bound state. [4] What information does this provide on the nucleon-nucleon force? [1] Energy is generated in the Universe by converting hydrogen into helium. Briefly describe two nuclear processes by which this is achieved and state which is favoured for low stellar temperatures. [c] [d] [5] Describe the () parameters used in the polar representation of a deformed quadrupole nuclear shape. [2] Which values of correspond to axially symmetric shapes? [1] Define what is meant by the term ‘triaxial nuclear shape’. [1] Define what is meant by the term K-isomer. [2] Such an isomeric state is observed in the nucleus 136 Sm (Z=62) based on a two-neutron configuration. Use the attached Nilsson diagram (Figure 1) to derive the structure of this isomeric state and determine its spin and parity Iπ. Assume ε2 ~ 0.2. [e] [4] Write down an expression relating the energy E(I) of a rotational level in a deformed even-even nucleus to its spin I, taking care to define your notations. Given that rotational frequency is defined as [2] , relate the rotational frequency to the -ray energy (i) for a quadrupole electromagnetic transition and (ii) for a dipole electromagnetic transition. PAPER CODE PHYS490 [3] Page 2 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 Figure 1: Nilsson diagram for neutrons, 50 N 82 (4 = 22/6). PAPER CODE PHYS490 Page 3 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 2. Answer either [a] or [b] [a] i) Consider the nuclear reaction: 7Li(p,n)7Be. What type of reaction is it? [1] Briefly discuss the main properties of such reactions and give two other examples. [4] ii) Given the following atomic mass excesses: 1 n 8071 keV 1 H 7289 keV 7 Li (Z=3) 14907 keV 7 Be (Z=4) 15769 keV calculate the Q-value for the 7Li(p,n)7Be reaction and explain under what circumstances the reaction will occur. [3] Give an expression for the threshold kinetic energy of the incident protons and compute its value in keV. [3] iii) For this reaction derive an expression for the velocity of the centre-of-mass in the laboratory frame. [2] At threshold, what is the neutron velocity in the laboratory? [1] Calculate the laboratory kinetic energy of the neutrons at threshold. [3] iv) Compute the values of TZ, ground-state isospin Tgs and all possible values of T for the 7Li and 7Be nuclei. [3] What isospin states in 7Be can be populated with the above reaction? Justify your answer. PAPER CODE PHYS490 [5] Page 4 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: [b] Dr. M. Chartier Physics TEL. NO. 07970247384 i) Explain what is meant by the terms ‘backbending’ and ‘band termination’. [5] ii) Briefly describe the spectra shown in Figures 2a and 2b, below. Briefly discuss what particular physical characteristics of 131Ce would result in such spectra. [3] Figure 2 iii) Using the data represented in Figure 2, determine the average rotational frequency and then the number of revolutions performed by the 131Ce (Z=58) nucleus during this decay. [5] iv) The rigid-body moment of inertia of a deformed (prolate) nucleus, of mass number A, may be estimated as: rigid = (2/5) MR2 (1 + 0.36β) where β denotes the usual quadrupole deformation parameter, and M and R are the mass and radius of the nucleus, respectively. PAPER CODE PHYS490 Page 5 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 Given β = 0.65, mN = 938.5 MeV/c2 (average nucleon mass), r0 = 1.2 fm (usual nuclear radius parameter), and c = 197 MeV.fm, calculate the associated rigid-body moment of inertia for the 131Ce nucleus. [4] v) The dynamic moment of inertia is expressed by: (2) = dI/dω = ħ2 [d2E(I)/dI2]1 Use the data represented in Figure 2 to calculate the value of (2) for the 131Ce nucleus. [3] vi) Compare and comment on the values obtained in questions 2 [b] iv) and 2 [b] v) above. [2] vii) From the data presented in Figure 2 and the results obtained above, what can you infer about the shape and structure of the 131Ce nucleus? Justify your answer. PAPER CODE PHYS490 [3] Page 6 of 7 Continued PAPER CODE NO. EXAMINER: PHYS490 DEPARTMENT: Dr. M. Chartier Physics TEL. NO. 07970247384 CONSTANTS Speed of light in vacuum c = 3.00 108 ms-1 Permeability of vacuum 0 = 4 10-7 Hm-1 = 4 10-7 VsA-1m-1 = 8.85 10-12 Fm-1 = 8.85 10-12 AsV-1m-1 Permittivity of vacuum 0 Elementary charge e = 1.60 10-19 C Planck constant h = 6.63 10-34 Js Avogadro constant NA = 6.02 1023 mol-1 Boltzmann constant k = 1.38 10-23 JK-1 Gas constant R = 8.31 JK-1mol-1 Unified atomic mass constant mu = 1.66 10-27 kg = 931.5 MeV/c2 = 9.11 10-31 kg = 0.511 MeV/c2 = 1.67 10-27 kg = 938.3 MeV/c2 Electron mass Proton mass me mp Gravitational constant G = 6.67 10-11 Nm2kg-2 Acceleration due to gravity g = 9.8 ms-2 Bohr magneton B = 9.27 10-24 JT-1 PAPER CODE PHYS490 Page 7 of 7 End
© Copyright 2024