1. The isotropic Fermi contact interaction, (A(r)FC) between the magnetic moment of a nucleus and the magnetic moment due to the unpaired electron spin is described by the following formula A(M)=C = 32 VeYxh(10-4)27*14() where ye is the gyromagnetic ratio of the electron, yn is the gyromagnetic ratio of the nucleus, h is the Planck's constant, ao is the Bohr radius, and 19 (0)2 is the probability density at position r. The position r is specified by the Cartesian coordinates (x, y, z). For every position (x, y, z), there is a corresponding value of 14 (0)12 One hundred thousand positions (x, y, z), and the corresponding values of 4 (1) are stored in a file psi_square.dat and the format is 4F 15.10. ye, yn, h, and a. are constants and the values are stored in a file constants.dat in free form. Write a complete Fortran program with the following specifications: i. Read in the values of (x, y, z), 19(0)12. Ye, yn, h, and a, from the two data files. Suitable action must be performed if any error is encountered when opening or accessing the files. For every (x, y, z), calculate the value of A(r)FC. Store the values of (x, y, z), and the corresponding values of 1902 and A(r)FC in a suitable form of storage. iv. Calculate the average values of A(r)FC. Write all values of (x, y, z) and 14(r)] to a file if the corresponding values of A(r)ec are larger than or equal to the average value of A(r)ec. V. Test your program rigorously using suitable data. (70/100 marks) 1. The isotropic Fermi contact interaction, (A(r)FC) between the magnetic moment of a nucleus and the magnetic moment due to the unpaired electron spin is described by the following formula A(M)=C = 32 VeYxh(10-4)27*14() where ye is the gyromagnetic ratio of the electron, yn is the gyromagnetic ratio of the nucleus, h is the Planck's constant, ao is the Bohr radius, and 19 (0)2 is the probability density at position r. The position r is specified by the Cartesian coordinates (x, y, z). For every position (x, y, z), there is a corresponding value of 14 (0)12 One hundred thousand positions (x, y, z), and the corresponding values of 4 (1) are stored in a file psi_square.dat and the format is 4F 15.10. ye, yn, h, and a. are constants and the values are stored in a file constants.dat in free form. Write a complete Fortran program with the following specifications: i. Read in the values of (x, y, z), 19(0)12. Ye, yn, h, and a, from the two data files. Suitable action must be performed if any error is encountered when opening or accessing the files. For every (x, y, z), calculate the value of A(r)FC. Store the values of (x, y, z), and the corresponding values of 1902 and A(r)FC in a suitable form of storage. iv. Calculate the average values of A(r)FC. Write all values of (x, y, z) and 14(r)] to a file if the corresponding values of A(r)ec are larger than or equal to the average value of A(r)ec. V. Test your program rigorously using suitable data. (70/100 marks)