1
Resonance pa ame e s o he eac ion 12C(d,p)13C in he icini y o 1450 keV
o accele a o ene gy calib a ion
L. Csed eki1*, G. Á. Szíki2, Z. Szikszai1, I. Kocsis2
1Ins i u e o Nuclea Resea ch, Hunga ian Academy o Sciences, MTA A omki
H-4001 Deb ecen, P.O. Box 51, Hunga y
2Uni e si y o Deb ecen, Facul y o Enginee ing, Depa men o Basic Technical S udies, H-
4028 Deb ecen, Ó eme ő u. 2-4, Hunga y
*) Co esponding au ho . Tel.: +36 52 509200; ax: +36 52 416181.
E-mail add ess: c[email p o ec ed] (L. Csed eki).
Abs ac
The obse ed esonance pa ame e s o he 12C(d,p)13C eac ion in he icini y o 1450
keV deu e on ene gy ha e been de e mined in a ho ough p ocedu e, i ing ou ecen
expe imen al exci a ion cu e, as well as ea lie li e a u e da a wi h he Roo So wa e
Package. The esul ing ene gy and wid h (FWHM) o esonance a e 1445.8 ± 0.2 keV and
5.3±0.4 keV, espec i ely. We p opose he applica ion o his esonance as a p ecise and
simple me hod o accele a o ene gy calib a ion when pe o ming DIGE analysis.
PACS: 29.30.-h; 25.45.-z; 82.80.Ej; 25.45.De
Keywo ds: 12C(d,p)13C eac ion, esonance pa ame e s, accele a o calib a ion, DIGE
In oduc ion and mo i a ion
The accu a e ene gy calib a ion o low ene gy pa icle accele a o s is a basic equi emen
in he ield o Ion Beam Analysis (IBA) and low ene gy nuclea physics.
Se e al absolu e me hods can be applied o pa icle accele a o ene gy calib a ion, o
example measu ing na ow nuclea eac ion esonances and/o neu on h eshold [1], using
2
non- esonan nuclea eac ions [2], c oss o e echniques a highe ene gies [3], and
echniques based on Ru he o d backsca e ing spec ome y (RBS) [4].
To ou bes knowledge, using deu e on beams, only he 16O(d,n)17F eac ion a 1829.2±0.6
keV h eshold ene gy has been applied o he p ecise absolu e ene gy calib a ion o
accele a o s [5]. The implemen a ion o he neu on h eshold eac ion is a he complica ed
since he high backg ound o neu ons om d+d eac ions can hide he small neu on yield
a ound he h eshold ene gy, as we obse ed ea lie [6]. The e o e, a na ow nuclea eac ion
esonance, de ec ing gamma- ays, is p e e able.
In ou labo a o y, we a e con inuously wo king on he p ecise de e mina ion o hick a ge
gamma ay yields and exci a ion unc ions o se e al nuclea eac ions o analy ical pu poses
[7-12].
In he amewo k o a Coo dina ed Resea ch P ojec o ganized by he In e na ional A omic
Ene gy Agency (IAEA-CRP) [13], we measu ed he exci a ion unc ion o he 3089 keV
gamma line o he 12C(d,pγ)13C eac ion, as well as o he pa icles om he 12C(d,p1)13C,
12C(d,p0)13C and 12C(d,d0)12C eac ions in he 0.74-2.0 MeV ene gy ange. The esul s we e
p esen ed in e . [12].
Fo he 12C+d nuclea eac ions in he s udied ene gy ange, a p onounced compound
nucleus mechanism is p esen besides he di ec mechanism. Consequen ly, ce ain esonances
appea in he exci a ion unc ion. Close o 1450 keV deu e on ene gy, a ai ly na ow and
qui e in ense esonance can be obse ed. The exis ence o his kind o na ow and s ong
esonance wi h well-de ined ene gy is unique among he deu e on induced nuclea eac ions.
As he p epa a ion o a ca bon a ge is simple, his nuclea esonance is a possible op ion o
accele a o ene gy calib a ion using gamma- ay de ec ion. Wi h his me hod, he necessi y o
measu ing a na ow p o on esonance be o e swi ching o a deu e on beam can be a oided.
Ne e heless, o apply his esonance o ene gy calib a ion, i s posi ion has o be de e mined
as accu a ely as possible. The ene gy o his esonance had been es ablished ea lie as
1449.5±1.5 keV wi h a wid h o 7.0±0.5 keV [14] based on he wo k o T y i e al. [15].
T y i’s wo k ocused on he angula dis ibu ions o p o ons, ob ained om he shape o he
Dopple -shi ed γ-lines, aiming o gain insigh o he complex cha ac e o he eac ion. The
esonance ene gy pa ame e s we e ob ained by a me iculous p ocedu e o exp essing he
di e en ial c oss-sec ions in e ms o Legend e polynomials and s udying he ene gy
dependence o he polynomial coe icien s [15, 16]. This wo k ga e in aluable in o ma ion on
he na u e o he eac ion; howe e , looking a all he p esen ime a ailable expe imen al
da a, we hink ha i is indispensable o e-assess his esonance and es ablish he esonance
3
ene gy (and he o he esonance pa ame e s) anew, wi h a s aigh o wa d app oach which is
also applicable in a ou ine analy ical se ing.
The obse ed shape o esonance in he exci a ion unc ion depends on se e al pa ame e s,
such as he ene gy o esonance (ER), he wid h o he esonance (Γ), he c oss sec ion a he
esonance ene gy (σR) and he loss o ene gy in he a ge (ξ). The dependence o he
exci a ion unc ion o hese pa ame e s was gi en in e . [17], and a de ailed ma hema ical
desc ip ion o he p oblem was also p esen ed he e.
Beside he compila ion and e alua ion o he exis ing li e a u e da a, we measu ed he
exci a ion unc ion o he 12C(d,pγ)13C, 12C(d,p1)13C and 12C(d,d0)12C eac ions in he 1410-
1500 keV ene gy ange using a sel -suppo ing ca bon oil wi h 20 µg/cm2 hickness.
Mo eo e , in o de o check he eliabili y o ou expe imen al se -up and he applied
i ing and e alua ing p ocess, he exci a ion unc ion o he 23Na(p,p’γ)23Na eac ion was
measu ed in he 1900-1959 keV ene gy ange and he pa ame e s o he 1931 keV esonance
we e de e mined and compa ed wi h li e a u e da a. This wo k was ca ied ou as a pa o he
measu emen o he exci a ion unc ion o he 23Na(p,p’γ)23Na eac ion in he 1800-3000 keV
ene gy ange. The inal exci a ion unc ion wi h he de ailed desc ip ion o he expe imen al
condi ion will be published la e .
Expe imen al p ocedu e
The measu emen s we e ca ied ou a he 5 MV Van de G aa accele a o o MTA
A omki. The a ailable ions o analysis a e H +, D +, and 4He +. The asso men o ions and
hei ene gy ange p o ided by he accele a o make i possible o apply mos o he ion beam
analy ical echniques: PIXE, PIGE, RBS, Scanning T ansmission Ion Mic oscopy (STIM),
Elas ic Recoil De ec ion Analysis (ERDA) e c.
A sel -suppo ing ca bon oil ( hickness: 1.0×1018 a om/cm2) wi h an e apo a ed palladium
laye on i s su ace ( hickness: 2.2×1017 a om/cm2) was used as a a ge o he measu emen
o he exci a ion unc ions o 12C+d eac ion. Due o some p ope ies o he sample, he
measu emen s o he 12C+d eac ion we e ca ied ou on he a ge wi h he op o he Pd laye ,
which caused a sys ema ic al e a ion in he esonance pa ame e s. The e o e, he co ec ion o
he esonance ene gy was necessa y based on he s opping powe o deu e on beam in he Pd
laye . The ene gy loss (4.4 keV) was calcula ed wi h he SRIM code [18].
4
Mo eo e , a hin ilm o NaCl ( hickness: 8.4×1017 a om/cm2) e apo a ed on a sel -suppo ed
hin ilm o Ag was used o he measu emen o he exci a ion unc ion o he
23Na(p,p’γ)23Na eac ion in he 1900-1959 keV ene gy ange. Since he pa ame e s o he
included 1931 keV esonance ha e well es ablished alues in he li e a u e, he eliabili y o
ou expe imen al a angemen , i ing and e alua ing p ocess could be checked.
The numbe o a ge nuclei was de e mined wi h RBS echnique using alpha beam o
1.5MeV ene gy. The unce ain y o a ge hickness de e mina ion was 2.5%. Fo he
de ec ion o gamma- ays, a Canbe a Model GR4025-7600SL coaxial ype HPGe de ec o
(c ys al: 59.5 mm diame e , 170 cm3 olume) was applied a an angle o 55° ela i e o he
inciden beam di ec ion wi h a dis ance o 9.5 cm be ween he on ace o he c ys al and he
a ge . Pa icles om Ru he o d backsca e ing and nuclea eac ion we e de ec ed wi h an
ORTEC Ion Implan ed Silicon de ec o wi h 13 keV ene gy esolu ion. Fo he elimina ion o
high in ensi y backsca e ed pa icles, we used a coppe collima o wi h a diame e o 3 mm in
on o he pa icle de ec o . The numbe o bomba ding pa icles (Np) was de e mined ia
he measu emen o he inciden cha ge on he a ge chambe , which was an ideal Fa aday
cup. Fo a mo e de ailed desc ip ion o he expe imen al se up and also o he p ocedu e o
he de e mina ion o he absolu e e iciency o HPGe de ec o (εabs) and he solid angle o he
Si de ec o (Ω), see e . [11]. The unce ain y o he de e mina ion o Np (s ochas ic and
sys ema ic unce ain ies oge he ) was aken in o accoun wi h 3%. The unce ain y o εabs and
Ω we e aken in o accoun also wi h 3%.
The ene gy o he beam, as well as i s ene gy s abili y was egula ly assessed measu ing
he 991.81±0.04 keV esonances in he 27Al(p,γ)28Si eac ion.
Da a i ing p ocess
The i ing p ocess o he exci a ion unc ion o he 12C+d and 23Na(p,p’γ)23Na eac ions
a ound he esonance ene gies (~1450 keV and ~1931 keV, espec i ely) was pe o med
using he Minui pa o he Roo So wa e Package [19] a e ca e ul backg ound sub ac ion.
This so wa e is capable o ake he unce ain ies o c oss sec ion da a in o accoun , hus o
calcula e he unce ain ies o he i ed esonance pa ame e s. We ollowed basically wo
di e en ways o backg ound sub ac ion.
In he case o he 12C+d eac ion, he exci a ion unc ion was i ed wi h he model unc ion
p(E) gi en by Equa ion 1 ypically in he 1440-1470 keV ene gy ange using linea
backg ound sub ac ion (see Equa ion 2).
5
𝑝(𝐸)=

𝑅

2(𝑡𝑎𝑛−1𝐸−𝐸𝑅

/2 −𝑡𝑎𝑛−1𝐸−𝐸𝑅−


/2 )

(1), 𝐼𝑖𝑛𝑏𝑔(𝐸)=𝑎𝐸+𝑏 (2)
whe e E is he inciden pa icle ene gy, Γ is he ull wid h o esonance a hal maximum
in ensi y, ER is he esonance ene gy, σR is he c oss sec ion a he esonance ene gy and ξ is
he loss o ene gy in he a ge . Figu e 1 shows an example o he i ed exci a ion unc ion in
he case o 12C(d,pγ)13C eac ion (ou measu emen ). Thus he exci a ion unc ion (exci (E))
can be modelled as:
𝑒𝑥𝑐𝑖𝑡(𝐸)=𝑝(𝐸)+𝑙𝑖𝑛𝑏𝑔(𝐸) (3)
We de i ed Equa ion 1 om Equa ion 14 in li e a u e [17] con e ing he exp essions o gi e
c oss sec ion alues ins ead o yields.
In he case o he 23Na(p,p’γ)23Na eac ion, he exci a ion unc ion was also i ed wi h he
model unc ion p(E) (equa ion 1.) ypically in he 1900-1959 keV ene gy ange a e he
sub ac ion o a wo o de polynomial backg ound (equa ion 4., Figu e 2).
𝑝𝑜𝑙𝑏𝑔(𝐸)=𝑐𝐸2+𝑑𝐸+𝑓, (4)
Thus, he exci a ion unc ion can be modelled as:
𝑒𝑥𝑐𝑖𝑡(𝐸)=𝑝(𝐸)+𝑝𝑜𝑙𝑏𝑔(𝐸), (5)
In he case o he exci a ion unc ion o T y i [15, 16] and Elekes [20], all he pa ame e s (ER,
σR, Γ, ξ) we e i ed oge he due o he uncon olled o ob iously inco ec a ge hicknesses
(ξ). In he case o ou ecen measu emen and e [12], because o he eliable expe imen al
a ge hickness da a, only h ee pa ame e s (ER, σR, Γ) we e i ed and ξ was a ixed
pa ame e . Fo he de ails o he compu a ions we e e o he so wa e manual, a ailable
online [Minui 2, F ed James and Ma hias Winkle , CERN,
Gene a/h p:// oo .ce n.ch/d upal/con en /minui 2-manual-600].
Resul s and discussion

6
Table 1 shows he in eg a ed esul o he i ing p ocess in he case o he ~1450 keV and
~1931 keV esonance o he 12C+d and 23Na(p,p’γ)23Na eac ions, espec i ely, complemen ed
wi h some o he expe imen al and li e a u e da a. The da a included in Table 1 a e he
ollowing:
 sou ce o da a,
 ype o nuclea eac ion,
 ene gy loss in he a ge a 1450 keV o 1931 keV inciden pa icle ene gy calcula ed
om published o measu ed expe imen al hickness da a using SRIM 2013 so wa e
( he gi en unce ain ies include he unce ain y o hickness measu emen (~3%) and
SRIM calcula ion (<4%).
 numbe o da a poin s in he esonan peak (expec ed minimum numbe o he i ing
p ocess is 4),
 pa ame e s i ed wi h Roo So wa e: esonance ene gy, esonance wid h, c oss
sec ion a he esonance ene gy, ene gy loss in he a ge a 1450 keV o 1931 keV
pa icle ene gy, squa e o he co ela ion coe icien (R2). We no e ha in he case o
ou measu emen s, he esonance ene gies we e co ec ed wi h he ene gy loss in he
palladium laye .
The calcula ed alues o ER=1931.80.1and Γ=5.70.2 in he case o he 23Na(p,p’γ)23Na
eac ion a e consis en (wi hin wo sigma unce ain y) wi h he li e a u e da a (ER=1930.70.8
and Γ=6.90.5 [21]). This esul con i ms he eliabili y o ou expe imen al se -up and he
applied i ing and e alua ing p ocess.
F om he da a o he 12C(d,pγ)13C eac ion ( e . 12, 15, 16, 20 and Csed eki e al.) in Table
1, we de e mined he esonance ene gy and wid h (FWHM) o he ~1450 keV esonance
calcula ing he weigh ed a e ages.
The inal unce ain y o he esonance ene gy and wid h was calcula ed as:
𝜎=√1
∑1
𝜎𝑖2
𝑛
𝑖=1 (7)
whe e σ is he e o o he weigh ed a e age, σi is he unce ain y o each pa ame e s.
The inal, accep ed da a a e he ollowing:
7
𝐸𝑅=1445.8 ± 0.2 keV ,

=5.3 ± 0.4 keV
To de e mine hese new alues, all he a ailable, well-es ablished expe imen al da a ha we
could ind in he li e a u e and we succeeded o i we e aken in o accoun . Some da a we e
omi ed om he i ing p ocess because o he ob iously inco ec ene gy calib a ion o
insu icien numbe o da a poin s in he esonan peak. Mo eo e , in one case we we e unable
o i he exci a ion unc ion. The omi ed da a a e p esen ed in Table 2.
In he case o pa icle p oduc ion c oss sec ions, he angula dependence o he eac ions
may a ec he obse ed esonance pa ame e s h ough he in e e ence o di e en
esonances. Thus, o de e mine he esonance pa ame e s, he complex desc ip ion o he
eac ion is necessa y, using R-ma ix calcula ions. Howe e , his ime-consuming and in-
dep h app oach is ha dly applicable in he IBA p ac ice.
Conclusion
In his wo k, we sys ema ically s udied he esonance o he 12C(d,pγ)13C eac ion in he
icini y o 1450 keV as a po en ial choice o accele a o ene gy calib a ion o deu e ons.
On he one hand, we measu ed he exci a ion unc ions o he 12C(d,pγ)13C, 12C(d,p1)13C
and 12C(d,d0)12C eac ions, simul aneously de ec ing he esul ing pa icles and gamma- ays.
On he o he hand, we collec ed he li e a u e da a on he ~1450 keV esonance o he abo e
eac ions.
On he basis o 5 di e en da ase s (3 om li e a u e and 2 om ou own measu emen s,
using gamma- ay de ec ion) o he egion a ound 1450 keV, applying a i ing and weigh ed
a e aging p ocess, we ob ained 1445.8± 0.2 keV and 5.3±0.4 keV o he esonance ene gy
and wid h, espec i ely. The i ing p ocess, which was pe o med wi h he Roo Ma hema ics
So wa e, p o ed o be capable o he de e mina ion o esonance ene gy, esonance wid h,
a ge hickness and c oss sec ion alue a esonance ene gy, simul aneously. We ecommend
he use o he abo e esonance – accep ing he newly de e mined 1445.8 ± 0.2 keV alue o
esonance ene gy – o he ene gy calib a ion o accele a o s o deu e on beams.
Acknowledgemen s
8
The suppo o he IAEA Coo dina ed Resea ch P ojec “Re e ence Da abase o Pa icle-
Induced Gamma- ay Emission (PIGE) Spec oscopy” (Con ac No. 16967/R1) is
acknowledged.
The au ho s would like o hank Micaela Fonseca o he p epa a ion o he sodium sample
and P o . Á.Z. Kiss o his aluable sugges ions.
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Figu e and Table cap ions:
Fig 1. Fi ing p ocess o he exci a ion unc ion o he 12C(d,pγ)13C eac ion a ound 1450 keV
deu e on ene gy. The expe imen al da a a e om ou own measu emen s de ec ing gamma
ays om he 3089 keV line. The ob ained ER=1451.3±0.2 keV should be co ec ed wi h he
Pd laye hickness. The co ec ion esul ed in he alue ER=1446.90.2 keV. E o A and B
dashed lines show he 1sigma unce ain y o he esonance ene gy.
Fig. 2 Fi ing p ocess o he exci a ion unc ion o he 23Na(p,p’γ)23Na eac ion a ~1931 keV.
The igu e includes he esul s o he i ing p ocess wi h he calcula ed and li e a u e da a o
esonance pa ame e s and also he polynomial backg ound. E o A and B dashed lines
co espond o he 1sigma unce ain y o he esonance ene gy.