Finite-size nucleus for small nuclei problematic for rnucleus #121
Description
Summary
I noticed that rwfnestimate and rmcdhf was producing a lot of NaNs when I was trying a simple helium calculation. I traced it back to rnucleus not handling finite nuclei very well for small masses, specifically, it is not able to reliably find a lower limit for the bracketing algorithm used to find the value of CPARM which is written to isodata.
Build steps
To aid in my debugging, I enabled a debug flag (-ffpe-trap=invalid) that halts execution when NaNs result from a calculation (so called signaling NaNs). I additionally added some printouts that let me follow the progress of the iterative algorithm:
diff --git a/configure.sh b/configure.sh
index 44d43309..062010e0 100755
--- a/configure.sh
+++ b/configure.sh
@@ -35,7 +35,7 @@ fi
# cmake ..
#
mkdir "${build_abspath}" && cd "${build_abspath}" \
- && cmake ${cmake_args} "${GRASP}" \
+ && cmake ${cmake_args} -DCMAKE_Fortran_FLAGS="-fallow-argument-mismatch" -DCMAKE_Fortran_FLAGS_DEBUG="-g -O0 -fcheck=all -fbacktrace -ffpe-trap=invalid" "${GRASP}" \
|| exit
# Note: we need to use spaces, not tabs, to indent in the heredoc.
diff --git a/src/appl/rnucleus90/estrms.f90 b/src/appl/rnucleus90/estrms.f90
index 75e1eb77..c3d7cab7 100644
--- a/src/appl/rnucleus90/estrms.f90
+++ b/src/appl/rnucleus90/estrms.f90
@@ -44,6 +44,7 @@
DNUMER = 1.0D00 + (10.0D00/3.0D00)*PABC**2 + (7.0D00/3.0D00)*PABC**4 - &
120.0D00*ABC**5*SKFUN(5,CBAM)
DDENOM = 1.0D00 + PABC**2 - 6.0D00*ABC**3*SKFUN(3,CBAM)
+ write(*,*) "CPARM:",CPARM,"SQTBF:",SQTBF,"DNUMER:",DNUMER,"DDENOM:",DDENOM
ESTRMS = CPARM*SQTBF*SQRT(DNUMER/DDENOM)
!
RETURN
diff --git a/src/lib/lib9290/nucpot.f90 b/src/lib/lib9290/nucpot.f90
index 0c27fc07..4f772499 100644
--- a/src/lib/lib9290/nucpot.f90
+++ b/src/lib/lib9290/nucpot.f90
@@ -62,7 +62,9 @@
SABC3 = 6.0D00*ABC3
DMSAS = -SABC3*S3MCBA
EN = 1.0D00 + ABC2*PI2 + DMSAS
+ write(*,*) "ABC2:", ABC2, "PI2:", PI2, "DMSAS:", DMSAS
ZBN = Z/EN
+ write(*,*) "EN: ", EN, "Z: ", Z, "ZBN: ", ZBN
!
SET = .FALSE.
DO I = 1, N
@@ -72,6 +74,8 @@
RBC = RI/C
IF (RBC <= 1.0D00) THEN
CALL ES (RMCBA, S2RCBA, S3RCBA)
+ write (*,*) ZBN, DMSAS, SABC3, S3RCBA, RBC, H3PHP, &
+ THABC2, S2RCBA, RBC
ZZ(I) = ZBN*(DMSAS + SABC3*S3RCBA + RBC*(H3PHP - THABC2*S2RCBA&
- 0.5D00*RBC*RBC))
ELSEThen, I built Grasp using ./configure --debug; cd build-debug; make install.
Example calculations
✅ He point charge
#!/bin/bash
rnucleus <<EOF
2 ! Atomic number
0 ! Mass number
0 ! Mass of nucleus
0 ! Nuclear spin (I) (in units of h / 2 pi)
0 ! Nuclear dipole moment (in nuclear magnetons)
0 ! Nuclear quadrupole moment (in barns)
EOF
cat isodataOutput:
Enter the atomic number:
Enter the mass number (0 if the nucleus is to be modelled as a point source:
Enter the mass of the neutral atom (in amu) (0 if the nucleus is to be static):
Enter the nuclear spin quantum number (I) (in units of h / 2 pi):
Enter the nuclear dipole moment (in nuclear magnetons):
Enter the nuclear quadrupole moment (in barns):
Atomic number:
2.0000000000000000
Mass number (integer) :
0.0000000000000000
Fermi distribution parameter a:
0.0000000000000000
Fermi distribution parameter c:
0.0000000000000000
Mass of nucleus (in amu):
0.0000000000000000
Nuclear spin (I) (in units of h / 2 pi):
0.0000000000000000
Nuclear dipole moment (in nuclear magnetons):
0.0000000000000000
Nuclear quadrupole moment (in barns):
0.0000000000000000
❌ He finite nucleus
#!/bin/bash
rnucleus <<EOF
2 ! Atomic number
4 ! Mass number
n ! Don't revise anything
4.00260325413 ! Mass of nucleus
0 ! Nuclear spin (I) (in units of h / 2 pi)
0 ! Nuclear dipole moment (in nuclear magnetons)
0 ! Nuclear quadrupole moment (in barns)
n ! Don't revise anything
EOF
cat isodataOutput:
Enter the atomic number:
Enter the mass number (0 if the nucleus is to be modelled as a point source:
The default root mean squared radius is 1.6755000352859497 fm; (Angeli)
the default nuclear skin thickness is 2.2999999999999998 fm;
Revise these values?
CPARM: 0.83775001764297485 SQTBF: 0.77459666924148340 DNUMER: 50.758064556226614 DDENOM: 5.1404547432635033
CPARM: 0.41887500882148743 SQTBF: 0.77459666924148340 DNUMER: 768.38487531999533 DDENOM: 21.404808011898069
CPARM: 0.20943750441074371 SQTBF: 0.77459666924148340 DNUMER: 16757.944177000674 DDENOM: 120.95953206929572
CPARM: 0.10471875220537186 SQTBF: 0.77459666924148340 DNUMER: 441925.60209049028 DDENOM: 809.53696522078098
CPARM: 5.2359376102685928E-002 SQTBF: 0.77459666924148340 DNUMER: 12832842.141349165 DDENOM: 5917.2517181843532
CPARM: 2.6179688051342964E-002 SQTBF: 0.77459666924148340 DNUMER: 391152780.14432883 DDENOM: 45237.383087204340
CPARM: 1.3089844025671482E-002 SQTBF: 0.77459666924148340 DNUMER: 12215858823.909081 DDENOM: 353756.64087188256
CPARM: 6.5449220128357410E-003 SQTBF: 0.77459666924148340 DNUMER: 386176226545.25677 DDENOM: 2797992.8831556449
CPARM: 3.2724610064178705E-003 SQTBF: 0.77459666924148340 DNUMER: 12282611955342.043 DDENOM: 22256710.369846832
CPARM: 1.6362305032089353E-003 SQTBF: 0.77459666924148340 DNUMER: 391848492561690.12 DDENOM: 177546758.17539367
CPARM: 8.1811525160446763E-004 SQTBF: 0.77459666924148340 DNUMER: 12520072953318270. DDENOM: 1418350367.7352693
CPARM: 4.0905762580223382E-004 SQTBF: 0.77459666924148340 DNUMER: 4.0033741405271456E+017 DDENOM: 11338716143.626560
CPARM: 2.0452881290111691E-004 SQTBF: 0.77459666924148340 DNUMER: 1.2805921244046672E+019 DDENOM: 90677397930.314819
CPARM: 1.0226440645055845E-004 SQTBF: 0.77459666924148340 DNUMER: 4.0971148548311849E+020 DDENOM: 725289890505.86890
CPARM: 5.1132203225279227E-005 SQTBF: 0.77459666924148340 DNUMER: 1.3109519800312548E+022 DDENOM: 5801802016166.0986
CPARM: 2.5566101612639613E-005 SQTBF: 0.77459666924148340 DNUMER: 4.1948467124009764E+023 DDENOM: 46412347825526.484
CPARM: 1.2783050806319807E-005 SQTBF: 0.77459666924148340 DNUMER: 1.3423190092903766E+025 DDENOM: 371290509644439.44
CPARM: 6.3915254031599034E-006 SQTBF: 0.77459666924148340 DNUMER: 4.2953697287356027E+026 DDENOM: 2970290985827261.0
CPARM: 3.1957627015799517E-006 SQTBF: 0.77459666924148340 DNUMER: 1.3745101371077032E+028 DDENOM: 23762195522326704.
CPARM: 1.5978813507899758E-006 SQTBF: 0.77459666924148340 DNUMER: 4.3984193570613774E+029 DDENOM: 1.9009703472349229E+017
CPARM: 7.9894067539498792E-007 SQTBF: 0.77459666924148340 DNUMER: 1.4074921011948786E+031 DDENOM: 1.5207741599715369E+018
CPARM: 3.9947033769749396E-007 SQTBF: 0.77459666924148340 DNUMER: 4.5039713749236330E+032 DDENOM: 1.2166184808514791E+019
CPARM: 1.9973516884874698E-007 SQTBF: 0.77459666924148340 DNUMER: 1.4412703041518611E+034 DDENOM: 9.7329444583105102E+019
CPARM: 9.9867584424373490E-008 SQTBF: 0.77459666924148340 DNUMER: 4.6120641159682680E+035 DDENOM: 7.7863542112482086E+020
CPARM: 4.9933792212186745E-008 SQTBF: 0.77459666924148340 DNUMER: 1.4758603799390337E+037 DDENOM: 6.2290828268385442E+021
CPARM: 2.4966896106093373E-008 SQTBF: 0.77459666924148340 DNUMER: 4.7227529963316222E+038 DDENOM: 4.9832660446068242E+022
CPARM: 1.2483448053046686E-008 SQTBF: 0.77459666924148340 DNUMER: 1.5112809237103945E+040 DDENOM: 3.9866127489398935E+023
CPARM: 6.2417240265233431E-009 SQTBF: 0.77459666924148340 DNUMER: 4.8360988996881049E+041 DDENOM: 3.1892901644536707E+024
CPARM: 3.1208620132616716E-009 SQTBF: 0.77459666924148340 DNUMER: 1.5475516389105689E+043 DDENOM: 2.5514321176836587E+025
CPARM: 1.5604310066308358E-009 SQTBF: 0.77459666924148340 DNUMER: 4.9521652301304205E+044 DDENOM: 2.0411456885951901E+026
CPARM: 7.8021550331541789E-010 SQTBF: 0.77459666924148340 DNUMER: 1.5846928713403902E+046 DDENOM: 1.6329165486554698E+027
CPARM: 3.9010775165770895E-010 SQTBF: 0.77459666924148340 DNUMER: 5.0710171846070988E+047 DDENOM: 1.3063332380360953E+028
CPARM: 1.9505387582885447E-010 SQTBF: 0.77459666924148340 DNUMER: 1.6227254984851279E+049 DDENOM: 1.0450665900735609E+029
CPARM: 9.7526937914427236E-011 SQTBF: 0.77459666924148340 DNUMER: 5.1927215942097774E+050 DDENOM: 8.3605327191672061E+029
CPARM: 4.8763468957213618E-011 SQTBF: 0.77459666924148340 DNUMER: 1.6616709099963082E+052 DDENOM: 6.6884261747652969E+030
CPARM: 2.4381734478606809E-011 SQTBF: 0.77459666924148340 DNUMER: 5.3173469117468740E+053 DDENOM: 5.3507409395848183E+031
CPARM: 1.2190867239303405E-011 SQTBF: 0.77459666924148340 DNUMER: 1.7015510117203891E+055 DDENOM: 4.2805927515768906E+032
CPARM: 6.0954336196517023E-012 SQTBF: 0.77459666924148340 DNUMER: 5.4449632374434702E+056 DDENOM: 3.4244742012251349E+033
CPARM: 3.0477168098258511E-012 SQTBF: 0.77459666924148340 DNUMER: 1.7423882359720268E+058 DDENOM: 2.7395793609655608E+034
CPARM: 1.5238584049129256E-012 SQTBF: 0.77459666924148340 DNUMER: 5.5756423550946682E+059 DDENOM: 2.1916634887666272E+035
CPARM: 7.6192920245646278E-013 SQTBF: 0.77459666924148340 DNUMER: 1.7842055536277645E+061 DDENOM: 1.7533307910109731E+036
CPARM: 3.8096460122823139E-013 SQTBF: 0.77459666924148340 DNUMER: 5.7094577716047970E+062 DDENOM: 1.4026646328078472E+037
CPARM: 1.9048230061411570E-013 SQTBF: 0.77459666924148340 DNUMER: 1.8270264869128876E+064 DDENOM: 1.1221317062459045E+038
CPARM: 9.5241150307057848E-014 SQTBF: 0.77459666924148340 DNUMER: 5.8464847581202011E+065 DDENOM: 8.9770536499657491E+038
CPARM: 4.7620575153528924E-014 SQTBF: 0.77459666924148340 DNUMER: 1.8708751225982988E+067 DDENOM: 7.1816429199720009E+039
CPARM: 2.3810287576764462E-014 SQTBF: 0.77459666924148340 DNUMER: 5.9868003923142910E+068 DDENOM: 5.7453143359773618E+040
CPARM: 1.1905143788382231E-014 SQTBF: 0.77459666924148340 DNUMER: 1.9157761255405308E+070 DDENOM: 4.5962514687817958E+041
CPARM: 5.9525718941911155E-015 SQTBF: 0.77459666924148340 DNUMER: 6.1304836017296309E+071 DDENOM: 3.6770011750253995E+042
CPARM: 2.9762859470955578E-015 SQTBF: 0.77459666924148340 DNUMER: 1.9617547525534709E+073 DDENOM: 2.9416009400203058E+043
CPARM: 1.4881429735477789E-015 SQTBF: 0.77459666924148340 DNUMER: 6.2776152081710899E+074 DDENOM: 2.3532807520162367E+044
CPARM: 7.4407148677388944E-016 SQTBF: 0.77459666924148340 DNUMER: 2.0088368666147459E+076 DDENOM: 1.8826246016129868E+045
CPARM: 3.7203574338694472E-016 SQTBF: 0.77459666924148340 DNUMER: 6.4282779731671827E+077 DDENOM: 1.5060996812903889E+046
CPARM: 1.8601787169347236E-016 SQTBF: 0.77459666924148340 DNUMER: 2.0570489514134975E+079 DDENOM: 1.2048797450323110E+047
CPARM: 9.3008935846736180E-017 SQTBF: 0.77459666924148340 DNUMER: 6.5825566445231908E+080 DDENOM: 9.6390379602584844E+047
CPARM: 4.6504467923368090E-017 SQTBF: 0.77459666924148340 DNUMER: 2.1064181262474207E+082 DDENOM: 7.7112303682067875E+048
CPARM: 2.3252233961684045E-017 SQTBF: 0.77459666924148340 DNUMER: 6.7405380039917474E+083 DDENOM: 6.1689842945654290E+049
CPARM: 1.1626116980842022E-017 SQTBF: 0.77459666924148340 DNUMER: 2.1569721612773588E+085 DDENOM: 4.9351874356523432E+050
CPARM: 5.8130584904210112E-018 SQTBF: 0.77459666924148340 DNUMER: 6.9023109160875482E+086 DDENOM: 3.9481499485218745E+051
CPARM: 2.9065292452105056E-018 SQTBF: 0.77459666924148340 DNUMER: 2.2087394931480154E+088 DDENOM: 3.1585199588174996E+052
CPARM: 1.4532646226052528E-018 SQTBF: 0.77459666924148340 DNUMER: 7.0679663780736494E+089 DDENOM: 2.5268159670539997E+053
CPARM: 7.2663231130262640E-019 SQTBF: 0.77459666924148340 DNUMER: 2.2617492409835678E+091 DDENOM: 2.0214527736431998E+054
CPARM: 3.6331615565131320E-019 SQTBF: 0.77459666924148340 DNUMER: 7.2375975711474170E+092 DDENOM: 1.6171622189145598E+055
CPARM: 1.8165807782565660E-019 SQTBF: 0.77459666924148340 DNUMER: 2.3160312227671734E+094 DDENOM: 1.2937297751316478E+056
CPARM: 9.0829038912828300E-020 SQTBF: 0.77459666924148340 DNUMER: 7.4112999128549550E+095 DDENOM: 1.0349838201053183E+057
CPARM: 4.5414519456414150E-020 SQTBF: 0.77459666924148340 DNUMER: 2.3716159721135856E+097 DDENOM: 8.2798705608425462E+057
CPARM: 2.2707259728207075E-020 SQTBF: 0.77459666924148340 DNUMER: 7.5891711107634739E+098 DDENOM: 6.6238964486740370E+058
CPARM: 1.1353629864103538E-020 SQTBF: 0.77459666924148340 DNUMER: 2.4285347554443117E+100 DDENOM: 5.2991171589392296E+059
CPARM: 5.6768149320517688E-021 SQTBF: 0.77459666924148340 DNUMER: 7.7713112174217973E+101 DDENOM: 4.2392937271513837E+060
CPARM: 2.8384074660258844E-021 SQTBF: 0.77459666924148340 DNUMER: 2.4868195895749751E+103 DDENOM: 3.3914349817211069E+061
CPARM: 1.4192037330129422E-021 SQTBF: 0.77459666924148340 DNUMER: 7.9578226866399204E+104 DDENOM: 2.7131479853768855E+062
CPARM: 7.0960186650647110E-022 SQTBF: 0.77459666924148340 DNUMER: 2.5465032597247745E+106 DDENOM: 2.1705183883015084E+063
CPARM: 3.5480093325323555E-022 SQTBF: 0.77459666924148340 DNUMER: 8.1488104311192785E+107 DDENOM: 1.7364147106412068E+064
CPARM: 1.7740046662661777E-022 SQTBF: 0.77459666924148340 DNUMER: 2.6076193379581691E+109 DDENOM: 1.3891317685129654E+065
CPARM: 8.8700233313308887E-023 SQTBF: 0.77459666924148340 DNUMER: 8.3443818814661412E+110 DDENOM: 1.1113054148103723E+066
CPARM: 4.4350116656654444E-023 SQTBF: 0.77459666924148340 DNUMER: 2.6702022020691652E+112 DDENOM: 8.8904433184829786E+066
CPARM: 2.2175058328327222E-023 SQTBF: 0.77459666924148340 DNUMER: 8.5446470466213286E+113 DDENOM: 7.1123546547863828E+067
CPARM: 1.1087529164163611E-023 SQTBF: 0.77459666924148340 DNUMER: 2.7342870549188251E+115 DDENOM: 5.6898837238291063E+068
CPARM: 5.5437645820818054E-024 SQTBF: 0.77459666924148340 DNUMER: 8.7497185757402405E+116 DDENOM: 4.5519069790632850E+069
CPARM: 2.7718822910409027E-024 SQTBF: 0.77459666924148340 DNUMER: 2.7999099442368769E+118 DDENOM: 3.6415255832506280E+070
CPARM: 1.3859411455204514E-024 SQTBF: 0.77459666924148340 DNUMER: 8.9597118215580062E+119 DDENOM: 2.9132204666005024E+071
CPARM: 6.9297057276022568E-025 SQTBF: 0.77459666924148340 DNUMER: 2.8671077828985620E+121 DDENOM: 2.3305763732804019E+072
CPARM: 3.4648528638011284E-025 SQTBF: 0.77459666924148340 DNUMER: 9.1747449052753984E+122 DDENOM: 1.8644610986243215E+073
CPARM: 1.7324264319005642E-025 SQTBF: 0.77459666924148340 DNUMER: 2.9359183696881275E+124 DDENOM: 1.4915688788994572E+074
CPARM: 8.6621321595028210E-026 SQTBF: 0.77459666924148340 DNUMER: 9.3949387830020079E+125 DDENOM: 1.1932551031195658E+075
CPARM: 4.3310660797514105E-026 SQTBF: 0.77459666924148340 DNUMER: 3.0063804105606425E+127 DDENOM: 9.5460408249565263E+075
CPARM: 2.1655330398757053E-026 SQTBF: 0.77459666924148340 DNUMER: 9.6204173137940561E+128 DDENOM: 7.6368326599652211E+076
CPARM: 1.0827665199378526E-026 SQTBF: 0.77459666924148340 DNUMER: 3.0785335404140980E+130 DDENOM: 6.1094661279721768E+077
CPARM: 5.4138325996892631E-027 SQTBF: 0.77459666924148340 DNUMER: 9.8513073293251135E+131 DDENOM: 4.8875729023777415E+078
CPARM: 2.7069162998446316E-027 SQTBF: 0.77459666924148340 DNUMER: 3.1524183453840363E+133 DDENOM: 3.9100583219021932E+079
CPARM: 1.3534581499223158E-027 SQTBF: 0.77459666924148340 DNUMER: 1.0087738705228916E+135 DDENOM: 3.1280466575217545E+080
CPARM: 6.7672907496115789E-028 SQTBF: 0.77459666924148340 DNUMER: 3.2280763856732532E+136 DDENOM: 2.5024373260174036E+081
CPARM: 3.3836453748057895E-028 SQTBF: 0.77459666924148340 DNUMER: 1.0329844434154410E+138 DDENOM: 2.0019498608139229E+082
CPARM: 1.6918226874028947E-028 SQTBF: 0.77459666924148340 DNUMER: 3.3055502189294113E+139 DDENOM: 1.6015598886511383E+083
CPARM: 8.4591134370144736E-029 SQTBF: 0.77459666924148340 DNUMER: 1.0577760700574116E+141 DDENOM: 1.2812479109209107E+084
CPARM: 4.2295567185072368E-029 SQTBF: 0.77459666924148340 DNUMER: 3.3848834241837171E+142 DDENOM: 1.0249983287367285E+085
CPARM: 2.1147783592536184E-029 SQTBF: 0.77459666924148340 DNUMER: 1.0831626957387895E+144 DDENOM: 8.1999866298938282E+085
CPARM: 1.0573891796268092E-029 SQTBF: 0.77459666924148340 DNUMER: 3.4661206263641263E+145 DDENOM: 6.5599893039150626E+086
CPARM: 5.2869458981340460E-030 SQTBF: 0.77459666924148340 DNUMER: 1.1091586004365204E+147 DDENOM: 5.2479914431320501E+087
CPARM: 2.6434729490670230E-030 SQTBF: 0.77459666924148340 DNUMER: 3.5493075213968654E+148 DDENOM: 4.1983931545056401E+088
CPARM: 1.3217364745335115E-030 SQTBF: 0.77459666924148340 DNUMER: 1.1357784068469969E+150 DDENOM: 3.3587145236045120E+089
CPARM: 6.6086823726675575E-031 SQTBF: 0.77459666924148340 DNUMER: 3.6344909019103901E+151 DDENOM: 2.6869716188836096E+090
CPARM: 3.3043411863337788E-031 SQTBF: 0.77459666924148340 DNUMER: 1.1630370886113248E+153 DDENOM: 2.1495772951068877E+091
CPARM: 1.6521705931668894E-031 SQTBF: 0.77459666924148340 DNUMER: 3.7217186835562395E+154 DDENOM: 1.7196618360855102E+092
CPARM: 8.2608529658344469E-032 SQTBF: 0.77459666924148340 DNUMER: 1.1909499787379966E+156 DDENOM: 1.3757294688684081E+093
CPARM: 4.1304264829172235E-032 SQTBF: 0.77459666924148340 DNUMER: 3.8110399319615893E+157 DDENOM: 1.1005835750947265E+094
CPARM: 2.0652132414586117E-032 SQTBF: 0.77459666924148340 DNUMER: 1.2195327782277086E+159 DDENOM: 8.8046686007578120E+094
CPARM: 1.0326066207293059E-032 SQTBF: 0.77459666924148340 DNUMER: 3.9025048903286674E+160 DDENOM: 7.0437348806062496E+095
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CPARM: 4.7414970675351228E-073 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.2754734146887975E+216
CPARM: 2.3707485337675614E-073 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.8203787317510380E+217
CPARM: 1.1853742668837807E-073 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.6563029854008304E+218
CPARM: 5.9268713344189036E-074 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.7250423883206643E+219
CPARM: 2.9634356672094518E-074 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.9800339106565315E+220
CPARM: 1.4817178336047259E-074 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.3840271285252252E+221
CPARM: 7.4085891680236294E-075 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.9072217028201801E+222
CPARM: 3.7042945840118147E-075 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.5257773622561441E+223
CPARM: 1.8521472920059074E-075 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.2206218898049153E+224
CPARM: 9.2607364600295368E-076 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 9.7649751184393223E+224
CPARM: 4.6303682300147684E-076 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.8119800947514578E+225
CPARM: 2.3151841150073842E-076 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.2495840758011663E+226
CPARM: 1.1575920575036921E-076 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.9996672606409330E+227
CPARM: 5.7879602875184605E-077 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.9997338085127464E+228
CPARM: 2.8939801437592303E-077 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.1997870468101971E+229
CPARM: 1.4469900718796151E-077 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.5598296374481577E+230
CPARM: 7.2349503593980756E-078 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.0478637099585262E+231
CPARM: 3.6174751796990378E-078 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.6382909679668209E+232
CPARM: 1.8087375898495189E-078 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.3106327743734567E+233
CPARM: 9.0436879492475945E-079 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.0485062194987654E+234
CPARM: 4.5218439746237973E-079 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 8.3880497559901231E+234
CPARM: 2.2609219873118986E-079 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.7104398047920985E+235
CPARM: 1.1304609936559493E-079 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.3683518438336788E+236
CPARM: 5.6523049682797466E-080 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.2946814750669431E+237
CPARM: 2.8261524841398733E-080 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.4357451800535544E+238
CPARM: 1.4130762420699366E-080 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.7485961440428436E+239
CPARM: 7.0653812103496832E-081 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.1988769152342748E+240
CPARM: 3.5326906051748416E-081 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.7591015321874199E+241
CPARM: 1.7663453025874208E-081 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.4072812257499359E+242
CPARM: 8.8317265129371040E-082 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.1258249805999487E+243
CPARM: 4.4158632564685520E-082 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 9.0065998447995898E+243
CPARM: 2.2079316282342760E-082 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.2052798758396718E+244
CPARM: 1.1039658141171380E-082 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.7642239006717374E+245
CPARM: 5.5198290705856900E-083 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.6113791205373900E+246
CPARM: 2.7599145352928450E-083 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.6891032964299120E+247
CPARM: 1.3799572676464225E-083 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.9512826371439296E+248
CPARM: 6.8997863382321125E-084 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.3610261097151437E+249
CPARM: 3.4498931691160563E-084 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.8888208877721149E+250
CPARM: 1.7249465845580281E-084 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.5110567102176919E+251
CPARM: 8.6247329227901407E-085 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.2088453681741536E+252
CPARM: 4.3123664613950703E-085 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 9.6707629453932284E+252
CPARM: 2.1561832306975352E-085 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.7366103563145827E+253
CPARM: 1.0780916153487676E-085 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.1892882850516662E+254
CPARM: 5.3904580767438379E-086 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.9514306280413330E+255
CPARM: 2.6952290383719190E-086 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.9611445024330664E+256
CPARM: 1.3476145191859595E-086 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.1689156019464531E+257
CPARM: 6.7380725959297974E-087 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.5351324815571625E+258
CPARM: 3.3690362979648987E-087 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.0281059852457300E+259
CPARM: 1.6845181489824493E-087 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.6224847881965840E+260
CPARM: 8.4225907449122467E-088 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.2979878305572672E+261
CPARM: 4.2112953724561234E-088 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.0383902644458137E+262
CPARM: 2.1056476862280617E-088 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 8.3071221155665100E+262
CPARM: 1.0528238431140308E-088 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.6456976924532080E+263
CPARM: 5.2641192155701542E-089 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.3165581539625664E+264
CPARM: 2.6320596077850771E-089 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.2532465231700531E+265
CPARM: 1.3160298038925386E-089 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.4025972185360425E+266
CPARM: 6.5801490194626928E-090 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.7220777748288340E+267
CPARM: 3.2900745097313464E-090 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.1776622198630672E+268
CPARM: 1.6450372548656732E-090 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.7421297758904538E+269
CPARM: 8.2251862743283660E-091 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.3937038207123630E+270
CPARM: 4.1125931371641830E-091 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.1149630565698904E+271
CPARM: 2.0562965685820915E-091 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 8.9197044525591232E+271
CPARM: 1.0281482842910457E-091 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.1357635620472986E+272
CPARM: 5.1407414214552287E-092 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.7086108496378389E+273
CPARM: 2.5703707107276144E-092 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.5668886797102711E+274
CPARM: 1.2851853553638072E-092 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.6535109437682169E+275
CPARM: 6.4259267768190359E-093 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.9228087550145735E+276
CPARM: 3.2129633884095180E-093 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.3382470040116588E+277
CPARM: 1.6064816942047590E-093 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.8705976032093270E+278
CPARM: 8.0324084710237949E-094 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.4964780825674616E+279
CPARM: 4.0162042355118974E-094 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.1971824660539693E+280
CPARM: 2.0081021177559487E-094 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 9.5774597284317544E+280
CPARM: 1.0040510588779744E-094 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.6619677827454036E+281
CPARM: 5.0202552943898718E-095 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.1295742261963228E+282
CPARM: 2.5101276471949359E-095 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.9036593809570583E+283
CPARM: 1.2550638235974680E-095 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.9229275047656466E+284
CPARM: 6.2753191179873398E-096 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.1383420038125173E+285
CPARM: 3.1376595589936699E-096 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.5106736030500138E+286
CPARM: 1.5688297794968349E-096 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.0085388824400111E+287
CPARM: 7.8441488974841747E-097 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.6068311059520089E+288
CPARM: 3.9220744487420873E-097 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.2854648847616071E+289
CPARM: 1.9610372243710437E-097 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.0283719078092857E+290
CPARM: 9.8051861218552184E-098 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 8.2269752624742853E+290
CPARM: 4.9025930609276092E-098 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 6.5815802099794283E+291
CPARM: 2.4512965304638046E-098 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.2652641679835426E+292
CPARM: 1.2256482652319023E-098 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.2122113343868341E+293
CPARM: 6.1282413261595115E-099 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.3697690675094673E+294
CPARM: 3.0641206630797557E-099 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.6958152540075738E+295
CPARM: 1.5320603315398779E-099 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.1566522032060591E+296
CPARM: 7.6603016576993893E-100 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.7253217625648472E+297
CPARM: 3.8301508288496947E-100 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.3802574100518778E+298
CPARM: 1.9150754144248473E-100 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.1042059280415022E+299
CPARM: 9.5753770721242367E-101 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 8.8336474243320179E+299
CPARM: 4.7876885360621183E-101 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 7.0669179394656143E+300
CPARM: 2.3938442680310592E-101 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 5.6535343515724914E+301
CPARM: 1.1969221340155296E-101 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 4.5228274812579932E+302
CPARM: 5.9846106700776479E-102 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 3.6182619850063945E+303
CPARM: 2.9923053350388240E-102 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.8946095880051156E+304
CPARM: 1.4961526675194120E-102 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 2.3156876704040925E+305
CPARM: 7.4807633375970599E-103 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.8525501363232740E+306
CPARM: 3.7403816687985300E-103 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.4820401090586192E+307
CPARM: 1.8701908343992650E-103 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: 1.1856320872468954E+308
CPARM: 9.3509541719963249E-104 SQTBF: 0.77459666924148340 DNUMER: Infinity DDENOM: Infinity
Program received signal SIGILL: Illegal instruction.
Backtrace for this error:
Program received signal SIGBUS: Access to an undefined portion of a memory object.
Backtrace for this error:
Here, we see the NaN occurs because we are trying to divide Infinity by Infinity. Running through a debugger, we see this happens when trying to find a lower limit for CPARM for the bracketing algorithm:
* thread #1, queue = 'com.apple.main-thread', stop reason = EXC_BAD_INSTRUCTION (code=1, subcode=0x1e601840)
frame #0: 0x00000001000050f4 rnucleus`estrms_ at estrms.f90:48:46
45 120.0D00*ABC**5*SKFUN(5,CBAM)
46 DDENOM = 1.0D00 + PABC**2 - 6.0D00*ABC**3*SKFUN(3,CBAM)
47 write(*,*) "CPARM:",CPARM,"SQTBF:",SQTBF,"DNUMER:",DNUMER,"DDENOM:",DDENOM
-> 48 ESTRMS = CPARM*SQTBF*SQRT(DNUMER/DDENOM)
49 !
50 RETURN
51 END FUNCTION ESTRMS
Target 0: (rnucleus) stopped.
warning: This version of LLDB has no plugin for the language "fortran90". Inspection of frame variables will be limited.
(lldb) bt
* thread #1, queue = 'com.apple.main-thread', stop reason = EXC_BAD_INSTRUCTION (code=1, subcode=0x1e601840)
* frame #0: 0x00000001000050f4 rnucleus`estrms_ at estrms.f90:48:46
frame #1: 0x00000001000051c8 rnucleus`getcpr_ at getcpr.f90:50:42
frame #2: 0x0000000100005e04 rnucleus`MAIN__ at geniso.f90:67:10
frame #3: 0x0000000100006618 rnucleus`main at geniso.f90:13:10
frame #4: 0x000000018abc20e0 dyld`start + 2360
✅ Xe finite nucleus
rnucleus <<EOF
54 ! Atomic number
131 ! Mass number
n ! Don't revise anything
131.170428596076 ! Mass of nucleus
0 ! Nuclear spin (I) (in units of h / 2 pi)
0 ! Nuclear dipole moment (in nuclear magnetons)
0 ! Nuclear quadrupole moment (in barns)
n ! Don't revise anything
EOF
cat isodataOutput:
Enter the atomic number:
Enter the mass number (0 if the nucleus is to be modelled as a point source:
The default root mean squared radius is 4.7807998657226562 fm; (Angeli)
the default nuclear skin thickness is 2.2999999999999998 fm;
Revise these values?
CPARM: 2.3903999328613281 SQTBF: 0.77459666924148340 DNUMER: 3.1001987503262654 DDENOM: 1.4738104922203277
CPARM: 9.5615997314453125 SQTBF: 0.77459666924148340 DNUMER: 1.1006149549187731 DDENOM: 1.0295723209700669
CPARM: 5.9759998321533203 SQTBF: 0.77459666924148340 DNUMER: 1.2657234387500615 DDENOM: 1.0757051859788953
CPARM: 4.1831998825073242 SQTBF: 0.77459666924148340 DNUMER: 1.5706996655253853 DDENOM: 1.1545042606209786
CPARM: 5.0795998573303223 SQTBF: 0.77459666924148340 DNUMER: 1.3748924850426643 DDENOM: 1.1047826031094967
CPARM: 5.5277998447418213 SQTBF: 0.77459666924148340 DNUMER: 1.3131979032671883 DDENOM: 1.0884794793050161
CPARM: 5.7518998384475708 SQTBF: 0.77459666924148340 DNUMER: 1.2879792662424656 DDENOM: 1.0817192374492073
CPARM: 5.6398498415946960 SQTBF: 0.77459666924148340 DNUMER: 1.3001862243622659 DDENOM: 1.0849986365390318
CPARM: 5.5838248431682587 SQTBF: 0.77459666924148340 DNUMER: 1.3065870868286245 DDENOM: 1.0867128643059558
CPARM: 5.6118373423814774 SQTBF: 0.77459666924148340 DNUMER: 1.3033609784070448 DDENOM: 1.0858493326169478
CPARM: 5.6258435919880867 SQTBF: 0.77459666924148340 DNUMER: 1.3017672512855101 DDENOM: 1.0854223960961389
CPARM: 5.6328467167913914 SQTBF: 0.77459666924148340 DNUMER: 1.3009751588461611 DDENOM: 1.0852101211716068
CPARM: 5.6363482791930437 SQTBF: 0.77459666924148340 DNUMER: 1.3005802979218253 DDENOM: 1.0851042803142934
CPARM: 5.6380990603938699 SQTBF: 0.77459666924148340 DNUMER: 1.3003831628538103 DDENOM: 1.0850514338220065
CPARM: 5.6372236697934568 SQTBF: 0.77459666924148340 DNUMER: 1.3004817057992313 DDENOM: 1.0850778509131647
CPARM: 5.6376613650936633 SQTBF: 0.77459666924148340 DNUMER: 1.3004324281814412 DDENOM: 1.0850646408293170
CPARM: 5.6378802127437666 SQTBF: 0.77459666924148340 DNUMER: 1.3004077939816143 DDENOM: 1.0850580369411544
CPARM: 5.6377707889187150 SQTBF: 0.77459666924148340 DNUMER: 1.3004201106974924 DDENOM: 1.0850613387891015
CPARM: 5.6378255008312408 SQTBF: 0.77459666924148340 DNUMER: 1.3004139522435485 DDENOM: 1.0850596878410954
CPARM: 5.6377981448749779 SQTBF: 0.77459666924148340 DNUMER: 1.3004170314465189 DDENOM: 1.0850605133090900
CPARM: 5.6378118228531093 SQTBF: 0.77459666924148340 DNUMER: 1.3004154918390334 DDENOM: 1.0850601005735907
CPARM: 5.6378186618421751 SQTBF: 0.77459666924148340 DNUMER: 1.3004147220397910 DDENOM: 1.0850598942069674
CPARM: 5.6378152423476422 SQTBF: 0.77459666924148340 DNUMER: 1.3004151069390371 DDENOM: 1.0850599973901853
CPARM: 5.6378135326003758 SQTBF: 0.77459666924148340 DNUMER: 1.3004152993889417 DDENOM: 1.0850600489818645
CPARM: 5.6378143874740090 SQTBF: 0.77459666924148340 DNUMER: 1.3004152031639657 DDENOM: 1.0850600231860190
CPARM: 5.6378148149108256 SQTBF: 0.77459666924148340 DNUMER: 1.3004151550514957 DDENOM: 1.0850600102881005
CPARM: 5.6378146011924173 SQTBF: 0.77459666924148340 DNUMER: 1.3004151791077294 DDENOM: 1.0850600167370594
CPARM: 5.6378147080516214 SQTBF: 0.77459666924148340 DNUMER: 1.3004151670796122 DDENOM: 1.0850600135125799
CPARM: 5.6378147614812235 SQTBF: 0.77459666924148340 DNUMER: 1.3004151610655537 DDENOM: 1.0850600119003402
CPARM: 5.6378147881960246 SQTBF: 0.77459666924148340 DNUMER: 1.3004151580585246 DDENOM: 1.0850600110942203
CPARM: 5.6378148015534251 SQTBF: 0.77459666924148340 DNUMER: 1.3004151565550102 DDENOM: 1.0850600106911605
CPARM: 5.6378148082321253 SQTBF: 0.77459666924148340 DNUMER: 1.3004151558032528 DDENOM: 1.0850600104896306
CPARM: 5.6378148115714755 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554273744 DDENOM: 1.0850600103888657
CPARM: 5.6378148132411505 SQTBF: 0.77459666924148340 DNUMER: 1.3004151552394347 DDENOM: 1.0850600103384831
CPARM: 5.6378148124063134 SQTBF: 0.77459666924148340 DNUMER: 1.3004151553334045 DDENOM: 1.0850600103636743
CPARM: 5.6378148119888944 SQTBF: 0.77459666924148340 DNUMER: 1.3004151553803895 DDENOM: 1.0850600103762698
CPARM: 5.6378148117801850 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554038816 DDENOM: 1.0850600103825678
CPARM: 5.6378148116758302 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554156280 DDENOM: 1.0850600103857166
CPARM: 5.6378148117280080 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554097549 DDENOM: 1.0850600103841421
CPARM: 5.6378148117019187 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554126915 DDENOM: 1.0850600103849295
CPARM: 5.6378148116888749 SQTBF: 0.77459666924148340 DNUMER: 1.3004151554141599 DDENOM: 1.0850600103853232
Enter the mass of the neutral atom (in amu) (0 if the nucleus is to be static):
Enter the nuclear spin quantum number (I) (in units of h / 2 pi):
Enter the nuclear dipole moment (in nuclear magnetons):
Enter the nuclear quadrupole moment (in barns):
Atomic number:
54.000000000000000
Mass number (integer) :
131.00000000000000
Fermi distribution parameter a:
0.52338755531043146
Fermi distribution parameter c:
5.6378148116888749
Mass of nucleus (in amu):
131.14080528131399
Nuclear spin (I) (in units of h / 2 pi):
0.0000000000000000
Nuclear dipole moment (in nuclear magnetons):
0.0000000000000000
Nuclear quadrupole moment (in barns):
0.0000000000000000