Input Data File

Input data are read from file tho.dat, which is shown in Table 2. The file consists of the first line, which contains only two numbers, below referred to as I1 and I2, followed by a sequence of identical lines, each of them defining one specific run of the code. All numbers containing a dot are type real, and those without a dot are type integer. In quotations there are four-character strings giving acronyms of the Skyrme forces. The code uses free format, so at least one space is needed in order to separate the input numbers.

Table 2: Input data file tho.dat.

(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)	(i)	(j)	(k)	(l)	(m)	(n)	(o)	(p)	(q)	(r)	(s)
$-$20	20
20	$-$2.	0.	$-$1	300	1	70	50	'SLY4'	$-$1	1	0	0.26	0.5	9	0	2	2	0.0001
20	$-$2.	0.	$-$1	300	1	72	50	'SLY4'	$-$1	1	0	0.26	0.5	9	0	2	$-$2	0.0001
20	$-$2.	0.	$-$1	300	1	74	50	'SLY4'	$-$1	1	0	0.26	0.5	9	0	$-$2	2	0.0001
20	$-$2.	0.	$-$1	300	1	76	50	'SLY4'	$-$1	1	0	0.26	0.5	9	0	$-$2	$-$2	0.0001
$-$14	$-$2.	0.	$-$1	300	1	78	50	'SKP '	$-$1	1	0	0.26	0.5	9	0	4	4	0.0001
0	$-$2.	0.	$-$1	300	1	70	50	'SLY4'	$-$1	1	0	0.26	0.5	9	0	0	0	0.0001

The code has three main regimes:

(i)	nucleus-after-nucleus,	defined by I1$<$0,
(ii)	file-after-file,	defined by I1$=$0,
(iii)	chain-after-chain,	defined by I1$>$0.

In the nucleus-after-nucleus regime, the code ignores the values of $\vert$I1$\vert$ and I2, and then performs one run for each line of the input data file that follows the first line. This is the simplest and most often used regime, illustrated by the example given in Table 1.

In the file-after-file regime, the code ignores the value of I2, and then reads the second line of the input data file, from where it takes all fields except from the values of ININ, $N$, and $Z$. Then it performs one run for each dnnn_zzz file found in the current directory. Files dnnn_zzz contain results of previous runs and are described below.

In the chain-after-chain regime, the code reads the second line of the input data file, from where it takes all fields except from the values of $N$, and $Z$. Then it performs one run for each nucleus in the chain of isotones or isotopes located between the bottom of the stability valley and the drip line. The bottom of the stability valley is parametrically defined as

$$f(N,Z) \equiv N - Z - 0.006(N+Z)^{5/3} = 0.$$ (80)

• If I2$>$0, the code calculates the chain of isotopes for the proton number $Z$=I1, starting with the lowest even neutron number $N$ satisfying $f(N,Z)$$>$0, and then step-by-step increasing the number of neutrons by two. Calculations continue until the neutron drip line is reached, and then the program stops.

• If I2$<$0, the code calculates the chain of isotones for the neutron number $N$=I1, starting with the lowest even proton number $Z$ satisfying $f(N,Z)$$<$0, and then step-by-step increasing the number of protons by two. Calculations continue until the proton drip line is reached, and then the program stops.

All lines of the input data file, after the first line, contain 19 fields each. Below we denote these fields by letters (a) - (s), as shown in the header of Table 2. The description of the fields is as follows:

• (a) Number of oscillator shells $N_{sh}$:
  • If $N_{sh}>0$, the code prints intermediate results at every iteration.
  • If $N_{sh}<0$, the code prints results at the first and last iterations only, and the module of the input value is used for $N_{sh}$.
  • If $N_{sh}=0$, the code stops. This value is used to indicate the end of the input data file.
  For $N_{sh}>14$, the code always begins with a short, 20-iteration run using $N_{sh}=14$, and the resulting fields then serve as a starting point for the calculation with the requested value of $N_{sh}$. For the THO-basis calculations, use of $N_{sh}<14$ is not recommended, because precision of the HO density profile can be insufficient for a reliable determination of the LST function.
• (b) Oscillator basis parameter $b_0$= $\sqrt{b_z^2+b_\bot^2}$:
  • If $b_0 >0$, the code uses this given value of $b_0$.
  • If $b_0 <0$, the code uses the default value of $b_0=\sqrt{2(\hbar^2/2m)/(41 f A^{-1/3})}$ for $f$=1.2.
• (c) Deformation $\beta_0$ of the HO basis. The value of $\beta_0$ defines the HO oscillator lengths through $b_\bot=b_0q^{-1/6}$, $b_z=b_0q^{1/3}$, and $q=\exp \left(3\sqrt{5/(16\pi)} \beta_0\right)$. In particular, the value of $\beta_0=0$ corresponds to the spherical HO basis.
• (d) The THO basis control parameter ILST:
  • If ILST= 0, the code performs the HO basis calculation only. If ININ$<0$, the file dnnn_zzz.hel is used as the starting point. If MAXI$>$0, at the end of the given run file dnnn_zzz.hel is stored.
  • If ILST= $-$1, the code performs the HO basis calculation followed by the THO basis calculation. If ININ$<0$, the file dnnn_zzz.hel is used as the starting point. If MAXI$>$0, at the end of the given run files dnnn_zzz.hel and dnnn_zzz.tel are stored.
  • If ILST= 1, the code performs the THO basis calculation only. File dnnn_zzz.tel must exist and is used as the starting point (only ININ$<$0 is allowed). If MAXI$>$0, at the end of the given run file dnnn_zzz.tel is stored.
• (e) Maximal number of iterations MAXI. If the negative number is read, the absolute value is used.
  • If MAXI$>$0, at the end of the given run files dnnn_zzz.hel and/or dnnn_zzz.tel are stored,
  • If MAXI$<$0, files dnnn_zzz.hel and dnnn_zzz.tel are not stored, and the module of the input value is used for MAXI.
• (f) The starting-point control parameter ININ:
  • If ININ= 1, the code starts from a default spherical field predefined within the code,
  • If ININ= 2, the code starts from a default prolate field predefined within the code,
  • If ININ= 3, the code starts from a default oblate field predefined within the code,
  • If ININ= $-$1, the code starts from file snnn_zzz.hel or snnn_zzz.tel,
  • If ININ= $-$2, the code starts from file pnnn_zzz.hel or pnnn_zzz.tel,
  • If ININ= $-$3, the code starts from file onnn_zzz.hel or onnn_zzz.tel.
• (g) Number of neutrons $N$.
• (h) Number of protons $Z$.
• (i) Skyrme force character*4 acronym, e.g., 'SIII', 'SKP ', 'SLY4', or 'SKM*'. If value 'READ' is read, the code reads the Skyrme force parameters from file forces.dat. An example of the file forces.dat is presented in Table 3.
• (j) The Lipkin-Nogami control parameter KINDHFB:
  • If KINDHFB= 1, Lipkin-Nogami correction not included,
  • If KINDHFB=$-$1, Lipkin-Nogami correction included.
• (k) The pairing-force control parameter IPPFORCE:
  • If IPPFORCE= 0, No pairing correlations (Hartree-Fock calculation),
  • If IPPFORCE= 1, Calculation for the density-dependent delta pairing force,
  • If IPPFORCE= 2, Calculation for the density-independent delta pairing force.
• (l) The quadrupole-constraint control parameter ICSTR. If ICSTR=0, the quadrupole constraint is not included, and the next two fields (m) and (n) are not used. If ICSTR=1, then:
  • (m) Constrained value of the quadrupole deformation $\bar{\beta}$. The value of $\bar{\beta}$ defines the constrained quadrupole moment $\bar{Q}$ in Eq. (78) through: ${\textstyle{\bar{Q}=\sqrt{\frac{5}{\pi}} <r^2>\bar{\beta}}}$. To be done: what is $<r^2>$.
  • (n) Parameter $\eta$ defining the stiffness $C_Q$ of the quadratic quadrupole constraint constant by $C_Q=\eta (41 A^{-1/3})/(8Ab_0^2<r^2>)$.
• (o) The number of gauge-angle points $L$ used for the particle number projection. Note that the code always performs the PNP, even if pairing correlations are not included.
• (p) The particle-number-shift control parameter ISHIFT. If, ISHIFT=0, the particle-number-projection is performed on $N$ and $Z$, and the next two fields (q) and (r) are not used. If ISHIFT=1, then:
  • (q) Neutron-number shift KDN, i.e., the projection is performed on neutron number $N$+KDN,
  • (r) Proton-number shift KDZ, i.e., the projection is performed on proton number $Z$+KDZ.
• (s) Requested precision of convergence SI (in MeV). Iterations stop when changes of all mean-field and pairing matrix elements between two consecutive iterations become smaller than the value of SI. Recommended value is $0.0001$.

Table 3: User-defined parameters of the Skyrme force, as given in the file forces.dat.

Value	Description
'SLY4'	Skyrme-force acronym
0	Tensor term (0-excluded, 1-included)
$-$0.2488913d+04	$t_0$
0.4868180d+03	$t_1$
$-$0.5463950d+03	$t_2$
0.1377700d+05	$t_3$
0.8340000d0	$x_0$
$-$0.3440000d0	$x_1$
$-$1.0000000d0	$x_2$
1.3540000d0	$x_3$
0.1230000d+03	$W_0$
6.0d0	$1/\alpha$
20.735530d0	$\hbar^2$/2m
0.160d0	$\rho_0$ (saturation density for pairing)
1.0d0	$\gamma$ (power of density for pairing)
60.0d0	$\bar{e}_{\max }$ (pairing cut-off energy)
0.5d0	$V_1$ (0-volume, 1-surface, 0.5-mixed)
$-$244.7200d0	$V_0$ (pairing strength)

After the solution is found, and if MAXI$>$0, the code stores files dnnn_zzz.hel (if the HO-basis run has been performed) and/or dnnn_zzz.tel (if the THO-basis run has been performed). Names of these files are automatically constructed based on the input-data parameters ININ, $N$, and $Z$, namely:

• d = `s', `p', or `o', for $\vert$ININ$\vert$ = 1, 2, or 3, respectively,
• nnn = three-digit value of $N$ with leading zeros included,
• zzz = three-digit value of $Z$ with leading zeros included.

These files can be used in a later run to restart calculations from previously found solutions. For example, file s070_050.tel contains results of the THO-basis calculation for $^{120}$Sn, which has been obtained by starting from a spherical field. Note that the name of the file reflects the starting deformation only, while it may, in fact, contain results for another deformation that has been obtained during the iteration.