Nuclear Data Section
International Atomic Energy Agency
P.O.Box 100, A-1400 Vienna, Austria
Memo CP-D/631
Date:
To:
From:

31 March 2010
Distribution
N. Otsuka, S. Takács

Subject:

Production thick target yield

The production (unsaturated, time-dependent) yield is proportional to the beam
current, but not proportional to the irradiation time. (e,g, irradiation for 1 hour with 2
μA does not give the same activity as 2 hours and 1 μA irradiation.. See also Eqs.(3)and (4) in the appendix.) The production yield is a function of the irradiation time andits unit should be Bq/μA rather than Bq/μA•hr. IAEA-TECDOC-1211 (ChargedParticle Cross Section Database for Medical Radioisotope Production. Diagnostic
Radioisotopes and Monitor Reactions) also does not put “hr” for the units ofproduction thick target yield. Therefore we propose to change the dimension of thisquantity (SF8=DT) from TTT to TTY. The affected is summarized in the table in nextpage.
We also propose the following rule:1) Because the production yield depends on irradiation time, the irradiation timeshould be coded in free text for production yield.
2) Compilers should not decide the quantity code and its unit codes based on theauthors’ notation because there is no consistency in their expression. It should be
decided by the definition of the data given (with consultation of authors when thedefinition is not clear in the article). If authors give production yield, it should be
coded by Bq/μA even if the authors use Bq/μA•hr.
3) Physical thick target yield is usually derived from integration of the excitation
function of cross section. Therefore we should not use DERIV in SF9 when authors
derived physical thick target yield from the experimental cross section measured inthe work.
Physical thick target yields are coded as production thick target yield:
D4083.005, D4109.003, 005, 007, 009, D4110.004, D4111.006-012, where modifier DT should be replaced by PHY.
Thick target yields defined in EXFOR is summarized in Appendix.

Proposed correction of dimension (Unit family)
Unit (Dict.25)
CodeDPS/MUAHR
GBQ/COULKBQ/MUAHR
MBQ/COUL
MBQ/MUAHR
MCI/MUAHR
MUCI/MUAHR
CI/AHR/MEV
MBQ/C/MEV
GBQ/MUAMBQ/MUA
MCI/MUA
MUCI/MUA
PART/MUAHR

Expansion
decays per Sec/micro-Ampere-hour
Giga-Becquerel/Coulomb
kilo-Becquerel/micro-Ampere-hour
Mega-Becquerel/Coulomb
Mega-Becquerel/micro-Ampere-hour
milli-Curie/micro-Ampere-hour
micro-Curie/micro-Ampere-HourCurie per Ampere-hour per MeV
Mega-Becquerel/Coulomb/MeV
Giga-Becquerel/micro-Ampere
Mega-Becquerel/micro-Ampere
milli-Curie/micro-Ampere
micro-Curie/micro-Ampere
particles/micro-Ampere-hour

Dim.
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTTE
TTTE
TTY
TTY
TTY
TTY
TTY

Should be

Quantities (Dict.236)
CodeExpansion

Dim.

,TTY/DA,,DT(Diff.prod.thick/thin target yield)

TTDA(CUM),TTY,,DT(M),TTY,,DT,TTY,,DT,TTY,,PHY
CUM,TTY,,DT
CUM,TTY,,PHY
CUM/UND,TTY,,DT
IND,TTY,,DT
IND/M+,TTY,,DT
IND/UND,TTY,,DT
M+,TTY,,DT
M+,TTY,,PHY
M+/UND,TTY,,DT
M-,TTY,,DT
UND,TTY,,DT,TTY,,TM(Production thick/thin target yld(assum.cum.
(Production thick/thin-target yld,(uncert.
(Production thick/thin-target yield)(Physical thick/thin-target yield)(Cum.production thick-target yield (unsat.))(Physical thick/thin-target yield,(Cumul.thick-target yield/unit time,undef.
(Indep.production thick/thin-target yld(Ind.production thick-target yld incl.isom.
(Indep.thick-target yield/unit time,undef.
(Thick-target yield per unit time incl.isom.
(Physical thick/thin-target yield incl.isom.
(Thick-targ.yld/unit time incl.isom.tr.,(Product.thick/thin target yield excl.isom.
(Thick-target yield per unit time, undef.
(Prod.thick target yield/1 MeV thn.)

TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTT
TTTEShould be
Unused.
Delete.
TTY
TTY
TTY

,TTY/DE,,DT(Diff.production thick target yield d/dE)

TTTE(CUM),TTY(M),TTY,TTY,TTY/DA
CUM,TTY
CUM/(M),TTY
CUM/M-,TTY
CUM/UND,TTY
IND,TTY
IND/M+,TTY
IND/UND,TTY
M+,TTY(Sat.thick/thin target yield(assumed cumul.
(Thick-target yield (uncert.if isom.trans.)(Saturated thick/thin-target yield)(Diff.satur.thick target yield d/dA)(Saturated cumul.thick/thin target yield)(Cum.thick-target yield (uncert.isom.trans.
(Cum.satur.thick-target yield,exclud.isom.
(Cumulative thick-target yield, undefined(Independent thick-target yield)(Ind.satur.thick/thin-target yld,incl.isom.
(Independent thick-target yield,undefined(Thick-target yield, incl. via isomeric

TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY

TTT

TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
TTY
Unused.
Delete.

M+/UND,TTY
M-,TTY
PAR,TTY
PAR,TTY,G
PAR,TTY/DA
SEQ,TTY
UND,TTY(Thick target yield,incl.isom.trans.,undef.
(Thick-target yield, excluding isomeric(Partial thick target yield)(Partial thick target gamma yield)(Partial differential thick target yield(Thick target yield for specified reaction(Thick target yield, undefined reaction)TTYTTY
TTYTTYTTYTTYTTYAppendix: Thick target yields
Definitions:
1. Thick target product yield
The number of produced nuclei by one incident particle (charge Z) isE0

 dE 
∫0 dE σ (E )ρ  dx −1

[nuclei/incident particle]

This is thick target product yield. The number of produced nuclei after irradiation by current I(t)for t is−1
1 t
 E0 dE ()()σρdt'It'dEE⋅ ∫ ∫
 dx 
 Ze 0 0

If the current I(t) is constant unit current (I(t) = 1) , we obtain number of produced nuclei afterirradiation by unit current for time t−1

Et 0
 dE dE σ (E )ρ N 0 (E 0 , t ) =
 .
∫
Ze 0
 dx 
Then the number of produced nuclei by unit current per unit time isn 0 (E 0 ) ≡dN 0 (E 0 , t ) 1 0
 dE =⋅ ∫ dE σ (E )ρ 
dtZe 0 dx E−1(1)This is also thick target product yield.

2. Physical thick target yield
The activity of thick target product yieldy ( E 0 ) = λn 0 ( E 0 )is defined as physical thick target yield (Y in IAEA-TECDOC-1211).

(2)

3. Production thick target yield
Considering decay of the produced nuclei, the number of living nuclei after irradiation by unit
current N(E 0 ,t) satisfies

dN ( E 0 , t )= n0 ( E 0 ) − λ N ( E 0 , t )dt. The solution of this equation isN t (E 0 ) ≡ N (E 0 , t ) = n0 (E 0 )1 − e − λt(3)λand its activity

At (E 0 ) = λN t (E 0 ) .

(4)

is defined as production thick target yield. From this definition, production thick target yielddepends on irradiation time.

Especially, the number of living nuclei after the unit time irradiation isN 1 (E 0 ) ≡ N (E 0 , t = 1) = n0 (E 0 )1 − e −λ(5)λand its activity is

A1 (E 0 ) = λN 1 (E 0 )(6), which is defined as A 1 in IAEA-TECDOC-1211.

4. Saturation thick target yield
After infinite irradiation by unit current, the number of living nuclei isN ∞ (E 0 ) ≡ N ∞ (E 0 , t → ∞ ) =n0 (E 0 )(7)

λIts activity

A∞ (E 0 ) = λN ∞ (E 0 )(8)is defined as saturation thick target yield (A 2 in IAEA-TECDOC-1211).
The relations between quantities defined in (1) - (8) are

At (E 0 ) = y (E 0 )1 − e − λtN t (E 0 ) = n0 (E 0 )λ= A1 (E 0 )1 − e − λt

λ1 − e − λt
= A∞ (E 0 ) 1 − e −λt−λ1− e= N 1 (E 0 )()1 − e − λt
= N ∞ ( E 0 ) 1 − e − λt
1 − e −λ()

Thick Target Yield for n0= 1.0 [nuclei/μA-hour]
2.5n0*tN(t), T1/2=0.2 h
N(t), T1/2=0.5 h

2.0

Yield [nuclei/μA]

N(t), T1/2=1 h

1.5

1.0

0.5

1.
8

1.
6

1.
4

1.
2

1.
0

0.
8

0.
6

0.
4

0.
2

0.0

Irradiation time [hour]

Figure: Time dependence of living number ofnuclei for four nuclides which n 0 (E 0 )=1.0[nuclei/ μ A-h]) but half-lives are different(T 1/2 =0.2, 0.5, 1 [h]) . Solid line gives n 0 (E 0 )t
(mumber of produced nuclei) in [nuclei/μA],
and dotted, dash-dotted, dashed lines areN t (E 0 ) (number of living nuclei) in [nuclei/μA]. N 1 (E 0 ) (number of living nuclei after 1hour irradiation) is 0.28, 0.54, 0.74 [nuclei/μA] for T 1/2 =0.2, 0.5, 1 [h] cases. N ∞ (E 0 )(number of living nuclei after infinite timeirradiation) is 0.29, 0.72, 1.40 [nuclei/μA]
for T 1/2 =0.2, 0.5, 1 [h] cases. See Eqs. (2), (4),(5) and (6) for definitions of n 0 (E 0 ), N t (E 0 ),N 1 (E 0 ) and N ∞ (E 0 ).

Units of thick target yield:- Thick target product yield defined in Eq.(1) is given in [nuclei/incident particle].
If we set the unit current and time as 1 [μA] and 1 [h], the decay constant is λ[h-1]),.and
Number of produced nuclei per 1 [h] per 1 [μA]:n0 (E0 ) [nuclei / μA-h]

Number of living nuclei after 1 [h] per 1 [μA]:

N 1 ( E 0 ) = n0 ( E 0 )Number of living nuclei after infinite time per 1 [μA]: N ∞ (E0 ) =1 − e −λn0 ( E 0 )λλ[nuclei/μA][nuclei/μA]

Multiplication of λ [h-1]/3600 [s/h] (convert [decays/h] to [decays/s] = [Bq]) leads toy (E 0 ) =λ3600

A1 (E 0 ) =A∞ (E 0 ) =n0 (E 0 ) [Bq/μA-h]

λ3600

λ3600

N 1 (E 0 ) = n0 (E 0 )N ∞ (E 0 ) =1 − e −λ 1 − e −λ=y (E 0 ) [Bq/μA]
3600
λn0 (E 0 ) y (E 0 )[Bq/μA]=λ3600

Example: 124Te(p,2n)123I T 1/2 =13.23 [h] at 30 MeV (Table 5.1.8b of TECDOC-1211 p191):
y = 289 [GBq/C]=1040 [MBq/μA-h] (1 [μA-h]=3600 [C]). λ = ln2/T 1/2 =0.05239 [h-1].This
leads toProduction thick target activity after 1 hour irradiation:
A 1 =[1-exp(-0.05239)]/0.05239×1040=1013 [MBq/μA]

Saturated thick target activity:
A ∞ =1040/0.05239=19851[MBq/μA] = 19.9 [GBq/μA]

Distribution:
blokhin@ippe.ru
chiba@earth.sgu.ac.jp
claes.nordborg@oecd.org
emmeric.dupont@oecd.org
ganesan@barc.gov.in
gezg@ciae.ac.cn
hasegawa@nea.fr
henriksson@near.fr
hongwei@ciae.ac.cn
jhchang@kaeri.re.kr
j.roberts@iaea.org
kaltchenko@kinr.kiev.ua
katakura.junichi@jaea.go.jp
kato@nucl.sci.hokudai.ac.jp
kirarlyb@atomki.hu
l.vrapcenjak@iaea.org
manuel.bossant@oecd.org
manokhin@ippe.ru
mmarina@ippe.ru
mwherman@bnl.gov
nicolas.soppera@oecd.org

nklimova@kinr.kiev.ua
n.otsuka@iaea.org
nrdc@jcprg.org
oblozinsky@bnl.gov
ogritzay@kinr.kiev.ua
otto.schwerer@aon.at
r.forrest@iaea.org
samaev@obninsk.ru
s.babykina@polyn.kiae.su
scyang@kaeri.re.krs.dunaeva@iaea.org
stakacs@atomki.hu
stanislav.hlavac@savba.sk
taova@expd.vniief.ru
tarkanyi@atomki.hu
varlamov@depni.sinp.msu.ru
vlasov@kinr.kiev.ua
vmclane@optonline.net
v.pronyaev@iaea.orgv.zerkin@iaea.org
yolee@kaeri.re.kr