data for PTV hyperfine paper
1. Calculations for Eq. (31)
Note: the n^2 and sqr(2) have not been included
2. OPtimization liberty basic program
By varying gamma in Eq. (13) - which is emult in this program - the aim is to minimize the difference between Eq. (23) at two consecutive n - which is ngraddiff in the program. This gives the optimum value of the exponent B in Eq. (22) - which is ngrad1 here. The output for nS1/2 states (gamma > 0) is shown below and in Table 2. The B values are then transferred to the main program in Section 3.
Set nn = 1 to 3; emult (gamma) when fine-tuned = 1.006942700
1S1/2
nn = 1
2S1/2
nn = 2
ngrad1 = -3.0000421859595616
ngraddiff = 3.0000421859595616
3S1/2
nn = 3
ngrad1 = -3.0000421859593240
ngraddiff = -0.0000000000002376
done
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3. main LIBerty basic program
There are 30 states that can be calculated by setting nn = 1 to 30. The NIST data and CODATA are included in the program. Once B has been found in the optimization program, the variable A in Eq. (22) is varied until agreement is obtained with the first hyperfine midpoint of the set of states in view. Output is shown in Section 4 below.
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4. output of main LIBerty basic program
The data output for the Liberty BASIC program in Section 3. For 30 states of hydrogen, with gamma > 0 and gamma < 0 for each, there are bound-state distances, proton speed adjustments, magnetic potential adjustments, and hyperfine shifts. All frequencies are in MHz.
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