EPJ manusc ip No.
(will be inse ed by he edi o )
On he ole o seconda y pions in spalla ion a ge s
Da ide Mancusi1a, Se gio Lo Meo23, Nicola Colonna4, Alain Bouda d5, Miguel An onio Co és-Gi aldo6, Joseph
Cugnon7, Jean-Ch is ophe Da id5, Syl ie Le ay5, Jo ge Le endegui-Ma co6, C is ian Massimi38, and Vasilis
Vlachoudis9
1Den-Se ice d’é ude des éac eu s e de ma héma iques appliquées (SERMA), CEA, Uni e si é Pa is-Saclay, F-91191, Gi -
su -Y e e, F ance
2ENEA, Resea ch Cen e “Ezio Clemen el”, I-40129 Bologna, I aly
3INFN, Sec ion o Bologna, I-40127 Bologna, I aly
4INFN, Sec ion o Ba i, I-70125 Ba i, I aly
5IRFU, CEA, Uni e si é Pa is-Saclay, F-91191, Gi -su -Y e e, F ance
6Uni e sidad de Se illa, Facul ad de Fisica, 41012 Se illa, Spain
7AGO depa men , Uni e si y o Liège, allée du 6 aoû 17, bâ . B5, B-4000 Liège 1, Belgium
8Physics and As onomy Dep . “Alma Ma e S udio um” - Uni e si y o Bologna, I-40126 Bologna, I aly
9Eu opean O ganiza ion o Nuclea Resea ch (CERN), CH-1211 Gene a, Swi ze land
Recei ed: Decembe 19, 2016
Abs ac We use pa icle- anspo simula ions o show ha seconda y pions play a c ucial ole o he
de elopmen o he had onic cascade and he e o e o he p oduc ion o neu ons and pho ons om hick
spalla ion a ge s. In pa icula , o he n_TOF lead spalla ion a ge , i adia ed wi h 20 GeV/c p o ons,
neu al pions a e in ol ed in he p oduc ion o ∼90% o he high-ene gy pho ons; cha ged pions pa icipa e
in ∼40% o he in eg al neu on yield. Ne e heless, pho on and neu on yields a e shown o be ela i ely
insensi i e o la ge changes o he a e age pion mul iplici y in he indi idual spalla ion eac ions. We
cha ac e ize his obus ness as a peculia p ope y o had onic cascades in hick a ge s.
PACS. 25.40.Sc Spalla ion eac ions – 24.10.Lx Mon e-Ca lo simula ions – 28.20.Gd Neu on anspo :
di usion and mode a ion
1 In oduc ion
In spalla ion eac ions, a high-ene gy ( >150 MeV) ligh
p ojec ile collides wi h a nucleus and on a e age leads
o he emission o a la ge numbe o pa icles, mos ly
neu ons. The spec um o spalla ion neu ons ex ends o
la ge ene gies, up o he ene gy o he incoming p ojec ile.
Fo his eason, spalla ion eac ions a e o en used o he
pu pose o gene a ing in ense high-ene gy neu on luxes
[1], as i is he case o ins ance in Accele a o -D i en Sys-
ems (ADS), subc i ical eac o co es ha a e kep in a
s eady s a e by neu ons p oduced by a spalla ion sou ce
[2].
Neu ons a e no he only pa icles ha a e emi ed
du ing spalla ion eac ions. P o ons and ligh cha ged pa -
icles (LCPs, A≤4) a e also p esen , as a e pions i
he p ojec ile ene gy is high enough. Spalla ion is ac u-
ally capable o p oducing (wi h a ying yields) all nuclei
ligh e han he a ge nucleus and close o he s abil-
i y alley, as well as a hand ul o nuclei hea ie han he
a ge nucleus (as amply demons a ed by se e al expe i-
aCo esponding au ho . E-mail add ess: da-
[email p o ec ed]
men al campaigns [see e.g. 3, Fig. 12]). All hese pa icles,
especially he ligh es ones (neu ons, p o ons, pions and
LCPs), a e capable o inducing seconda y nuclea eac-
ions in a hick spalla ion a ge , and may hus con ibu e
o he de elopmen o he had onic cascade, o pa icle
emission and o he p oduc ion o esidual nuclei [see e.g.
4].
The s anda d heo e ical ool o he desc ip ion o
spalla ion eac ions is a hyb id nuclea - eac ion model whe e
an in anuclea -cascade (INC) s age is ollowed by an op-
ional p e-equilib ium s age and by a s a is ical de-exci a ion
s age [1]. Fo he easons e oked in he p e ious pa a-
g aph, hese models mus be alida ed no only o he
p ima y eac ions ( ypically eac ion be ween as p o ons
and hea y nuclei such as ungs en, lead o bismu h), bu
also o all seconda y eac ions ha may sizably con ibu e
o he p oduc ion o neu ons o o any o he obse able
one may be in e es ed in. I is gene ally acknowledged ha
seconda y p o on- and neu on-nucleus eac ions a e im-
po an , as sugges ed by he selec ion o alida ion da a
o in e na ional nuclea - eac ion-model in e compa isons
[5–7]; howe e , he same in e compa isons de o ed li le
a en ion o he p oduc ion o seconda y pions and o he
a Xi :1603.05453 3 [nucl- h] 16 Dec 2016
2 Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s
alida ion o models on pion-induced eac ions. This is a
leas pa ly due o he ac ha inclusi e da a o pion-
nucleus eac ions a e sca ce, and pa ly o he ac ha
ADSs a e expec ed o ope a e a ene gies o he o de o
1GeV [2], whe e pion mul iplici ies a e ela i ely low.
Se e al spalla ion neu on sou ces a e cu en ly ope a-
ional a ound he wo ld and mo e a e unde cons uc ion
o planned o he nea u u e. P edic ions o he neu on-
sou ce cha ac e is ics can ypically be ob ained by means
o Mon e Ca lo (MC) simula ions. Reliable esul s equi e
de ailed and accu a e knowledge o he physical p ocesses
a he basis o he spalla ion eac ions. Among he cu -
en ly ope a ing spalla ion neu on sou ces, he n_TOF
(neu on Time-O -Fligh ) acili y [8] is an in ense pulsed
neu on sou ce loca ed a CERN. Neu ons a e p oduced
by spalla ion o lead nuclei caused by an inciden 20 GeV/c
p o on beam, and subsequen ly mode a ed and collima ed
owa ds wo expe imen al a eas, whe e hei ene gy can be
measu ed using he ime-o - ligh echnique. One o he
o emos ad an ages o he de ec ion capabili y o n_-
TOF is ha he p oduced neu ons ex end o e mo e
han wel e o de s o magni ude, om he mal ene gies
o he GeV ange, allowing highly accu a e measu emen s
o a wide ange o applica ions. P ecise cha ac e iza ion
o he neu on sou ce is c ucial o hese pu poses, and
some ea u es o he neu on beam mus be ine i ably
de e mined ia nume ical simula ions [9]. In ecen publi-
ca ions [10, 11], he Gean 4 oolki o pa icle anspo
[12, 13] was used o cha ac e ize he neu on and pho on
luxes di ec ed owa ds he n_TOF expe imen al a eas.
Calcula ions o neu on and pho on luences pe o med
wi h di e en Gean 4 physics lis s exhibi ed la ge ela i e
di e ences. The au ho s sugges ed a he ime ha his
di e ence could be ela ed o di e en ea men s o pion
p oduc ion and pion-induced eac ions.
In his wo k, we s udy he ole o pion p oduc ion and
i s in luence on he spalla ion yields. In pa icula , i will
be shown ha seconda y pions play a c ucial ole o pa -
icle p oduc ion in hick spalla ion a ge s, such as he
n_TOF neu on sou ce. We shall demons a e ha he
p oduc ion o high-ene gy p omp pho ons is essen ially
domina ed by π0decay; his phenomenon is well known in
he con ex o he phenomenology o calo ime ic measu e-
men s o high-ene gy physics [14]. A he same ime, he
p oduc ion o neu ons is a ec ed by bo h seconda y π±-
nucleus eac ions and π0p oduc ion. These ac s no wi h-
s anding, pa icle yields a e less sensi i e o he de ail o
he speci ic nuclea - eac ion model used o he pa icle-
anspo simula ion. This is explained in e ms o an in-
insic “ esilience” o had onic cascades in hick a ge s.
The pape is s uc u ed as ollows. In Sec. 2 we p o-
ide a b ie desc ip ion o he salien ea u es o he Liège
In anuclea -Cascade model (INCL), which is pi o al o
ou nume ical simula ions o he n_TOF spalla ion a -
ge . Thin- a ge model calcula ions ela ed o he pion
sec o a e p esen ed and discussed in Sec. 3, along wi h
compa isons agains expe imen al da a. Sec ion 4 shi s
he ocus owa ds he hick- a ge anspo calcula ions
o he n_TOF spalla ion a ge . The mos impo an ea-
u es o he MC simula ions, desc ibed in de ail in ecen
pape s [10, 11], a e ecalled in Secs. 4.1 and 4.2. The ole
played by pions in he emission o neu ons and pho ons
is highligh ed in Secs. 4.3–4.5. Sec ion 4.7 illus a es he
endency o he had onic cascade o mi iga e he sensi i -
i y o he pa icle yields o he de ails o he desc ip ion
o he nuclea eac ions. Conclusions a e d awn in Sec. 5.
2 Model desc ip ion: he Liège In anuclea
Cascade model
The Liège In anuclea Cascade model (INCL) [15, 16] is
one o he mos e ined exis ing ools o he desc ip ion
o spalla ion eac ions. The model is cu en ly main ained
and de eloped join ly by he Uni e si y o Liège (Belgium)
and CEA (Saclay, F ance). The model assumes ha he
i s s age o he eac ion can be desc ibed as an a alanche
o independen bina y collisions. The INCL model is essen-
ially classical, wi h he addi ion o a ew sui able ing edi-
en s ha mimic genuine quan um-mechanical ea u es o
he ini ial condi ions and o he dynamics: o ins ance,
a ge nucleons a e endowed wi h Fe mi mo ion, ealis-
ic space densi ies a e used, he ou pu o bina y colli-
sions is andom and elemen a y nucleon-nucleon collisions
a e subjec o Pauli blocking. The model can desc ibe he
emission o nucleons and pions; ligh clus e s (up o Z= 5,
A= 8 by de aul ) can also be p oduced h ough a dynam-
ical phase-space coalescence algo i hm.
In anuclea -cascade models in gene al (and INCL in
pa icula ) only desc ibe he as , dynamical s age o a
spalla ion eac ion, leading o he o ma ion o exci ed
nuclei which subsequen ly de-exci e by emi ing pa icles
and/o issioning. I is he e o e necessa y o ollow he
de-exci a ion o his cascade emnan i one equi es a
comple e desc ip ion o he nuclea eac ion. Since he
ime scale o de-exci a ion is much longe han o cas-
cade, a di e en physical desc ip ion is usually employed.
This may include an op ional p e-equilib ium s age, which
hen handles he he maliza ion o he emnan ; i p e-
equilib ium is used, he in anuclea -cascade s age is s opped
ea lie . Ei he way, he maliza ion is a ained and subse-
quen de-exci a ion o he emnan is desc ibed by s a-
is ical de-exci a ion models. Wi hin Gean 4, INCL can
be di ec ly coupled wi h wo di e en de-exci a ion codes,
namely: G4Exci a ionHandle , he na i e s a is ical de-
exci a ion model o Gean 4 and he de aul choice [17],
and ABLA V3, a de-exci a ion model de eloped a GSI
(Da ms ad , Ge many) [18, 19]. We s ess he e ha his
is no he code ha is usually coupled o INCL (which
is ABLA07 [20]), bu a he an olde e sion. A de ailed
compa ison o he capabili ies o he wo e sions can be
ound in Re . 20.
Di e en pa icles a e p oduced in di e en s ages o
he spalla ion eac ions. In pa icula , while neu ons and
γ- ays a e mos ly gene a ed in de-exci a ion p ocesses,
pion p oduc ion, in pa icula , occu s en i ely in he i s
eac ion s age. The pion dynamics in INCL has been e-
cen ly upg aded o push he uppe ene gy limi o he
Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s 3
model up o 15–20 GeV. Olde e sions o INCL consid-
e ed only one mechanism o pion p oduc ion, namely ex-
ci a ion and subsequen decay o he ∆(1232) esonance.
Fo nucleon-induced eac ions, his is a good app oxima-
ion up o ene gies o abou 2–3GeV. This is p o en by
he esul s o he IAEA benchma k [5–7], as well by he
p e ious s udies on he INCL pion dynamics [21, 22]. Ad-
di ionally, one should no o ge ha , as soon as mul iple
collisions a e in ol ed, any pa icle co ela ion due o he
ac ion o an in e media e esonance will be washed ou .
Fo he pu pose o co ec ly desc ibing mul iple-collision
eac ions, i is su icien o cap u e he i s -o de beha -
io , and co ela ions may be neglec ed. O cou se, selec-
i e o exclusi e obse ables (such as wo-pa icle co e-
la ions), especially i ela ed o one- o ew-collision eac-
ions will gene ally be inco ec ly desc ibed.
Abo e 2–3GeV, exci a ion o hea ie ba yonic and
mesonic esonances becomes likely1. A s aigh o wa d ex-
ension o INC would in p inciple en ail he desc ip ion
o all he ene gy-angle-di e en ial c oss sec ions o he
o ma ion, sca e ing and abso p ion o he esonances in
he nuclea medium, as well as hei mean- ield po en-
ials, decay modes, e c. The amoun o in o ma ion ha
mus be ed in o he model is ponde ous; besides, mos o
he ime, he a ailable expe imen al in o ma ion on hese
elemen a y p ocesses is di ely sca ce, o pa ial a bes .
One possible app oach would be o ely on an indepen-
den e en gene a o o he elemen a y had on-nucleus
collisions, in he spi i o Re . 23. In his pape , howe e ,
we explo e a di e en solu ion.
I should be no ed ha ba yonic esonances abo e
∆(1232) a e la gely o e lapping. This aises he ques ion
o whe he i is meaning ul o conside hem as ha ing
sepa a e iden i ies in he amewo k o INC. Addi ionally,
hei li e ime (in acuum) is much smalle han he ypi-
cal ime be ween subsequen collisions du ing INC (a ew
m/c), so ha a hea y esonance is unlikely o unde go
any collision be o e decaying in he nucleus. This is al-
eady ma ginally he case o ∆(1232), whose li e ime in
acuum is ∼1.6 m/c, and indeed mos o he obse ables
calcula ed in INC a e a he insensi i e o a ia ions o he
∆(1232) li e ime. I should also be conside ed ha he i-
nal (on he ime scale o INC) decay p oduc s o ba yonic
esonances a e o en pions.
S ic ly speaking, he a gumen s abo e do no apply
o mos o he ligh es un la o ed mesonic esonances (η,
ω,η0. . . ), whose li e imes a e compa able o o longe
han he du a ion o he INC s age; no do hey apply
o s ange ba yons and mesons (Λ,Σ,K. . . ), which un-
de go weak decay. Howe e , he a ailable expe imen al el-
emen a y c oss sec ions associa ed wi h he p oduc ion o
hese pa icles [24, 25] and o de -o -magni ude es ima es
sugges ha hei global in luence on he INC dynamics
1The exci a ion o he Rope N∗(1440) esonance is a spe-
cial excep ion, because i may be exci ed a lowe ene gy in
he T= 0 channel. INCL4.6 assumes ha he kinema ics o
pion p oduc ion in his channel is go e ned by he ∆(1232)
esonance. The ex ended e sion o INCL does no make his
app oxima ion.
is weak. The e o e, i should be possible o ea hem as
co ec ions, a leas in he ene gy ange up o 10–15 GeV.
In iew o he discussion abo e, i is app op ia e o
use a mo e p agma ic app oach o he desc ip ion o high-
ene gy eac ions. In he la es e sion o he INCL model,
he p oduc ion and decay o indi idual esonances (ex-
cep o ∆(1232)) is bypassed and eplaced by mul ipion
collisions, i.e. e ec i e wo-body collisions leading o he
p oduc ion o one o mo e pions in he inal s a e, o he
ollowing o m:
N+N→N+N+xπ, (1a)
π+N→N+xπ. (1b)
In he cu en model, he numbe xo pions in he inal
s a e o he collision akes all alues om 1 o 4inclusi e.
The es o he pion dynamics in he new e sion o
INCL is he same as in he olde one. The o ma ion, ab-
so p ion and decay o he ∆(1232) esonance is explici ly
ea ed. Pion abso p ion is possible only ia he o ma-
ion o ∆(1232). No one-s ep mechanism o pion abso p-
ion on nucleon pai s is included. Fu he de ails on he
la es e sion o INCL can be ound in Re s. 26, 27. Rela-
i e o he published e sion, he cu en implemen a ion
o he model has sligh ly e ol ed, wi h he mos no able
di e ence conce ning he biasing o nucleons owa ds he
o wa d di ec ion in he cen e -o -mass sys em2.
The e ec o he mul ipion ex ension can be s udied
by compa ing some global quan i ies calcula ed wi h he
old (INCL4.6) and he new ex ended model (INCL++).
Figu e 1 shows he a e age pion mul iplici y (i.e. he a -
e age numbe o pions p oduced pe inelas ic eac ion) in
p+208Pb as a unc ion o he p o on ene gy. While he wo
models yield simila p edic ions a low p ojec ile ene gy, in
he olde model he mul iplici y sa u a es a ound 5GeV,
ne e exceeding ∼1pion pe eac ion, while he ex ended
model yields an almos linea inc ease up o 20 GeV. Fig-
u e 2 shows how he p oduced pions a e dis ibu ed o e
he h ee cha ge s a es, acco ding o he calcula ions o he
ex ended model. The ac ion o neu al pions is oughly
ene gy-independen . On he con a y, he lines o posi-
i e and nega i e pions c oss be ween 4and 5GeV. The
supp ession o nega i e pions a low ene gy can be ex-
plained by conside ing ha he p ojec ile (a p o on) ca -
ies posi i e isospin, and ha pions can only be p oduced
in he i s ew collisions. As he ene gy and he numbe o
collisions inc ease, pion p oduc ion becomes inc easingly
domina ed by he o al isospin o he sys em, which is
2In he cu en model, he inal-s a e pa icle momen a a e
gene a ed acco ding o a la , unbiased phase-space sampling
algo i hm. Le Ebe he gene a ed CM ene gy o he i s nu-
cleon; he alue o Ede e mines he minimum ( min) and max-
imum ( max) alues o he Mandels am ou -momen um ans-
e . The alue o is hen sampled om a dis ibu ion o
he o m exp (B )and all he gene a ed momen a a e o a ed
o ma ch he sampled ou -momen um ans e o he i s
nucleon. Clea ly his algo i hm does no modi y he single-
pa icle ene gy dis ibu ions in he CM sys em, which a e
he e o e s ill gi en by he phase-space model. On he o he
hand, he dis ibu ions in he labo a o y sys em a e di e en .
4 Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s
0 5 10 15 20
p o on ene gy (GeV)
0
2
4
6
8
10
12
a e age mul iplici y
neu ons ×0.25
p o ons
pions
INCL++
INCL4.6
Figu e 1. Exci a ion unc ion o he o al a e age neu on,
p o on and pion mul iplici ies ( om in anuclea cascade and
de-exci a ion) in he inal s a e o p+208Pb eac ions, as cal-
cula ed wi h (INCL++) and wi hou (INCL4.6) mul ipion ex-
ension, coupled wi h ABLA07. No e ha he neu on cu e
has been eno malized by a ac o o 0.25.
0 5 10 15 20
p o on ene gy (GeV)
0.0
0.1
0.2
0.3
0.4
ac ion
π+
π0
π−
Figu e 2. Exci a ion unc ions o he a e age ac ion o p o-
duced pions o each o he h ee cha ge s a es, in p+208Pb, as
calcula ed by INCL++.
nega i e because N > Z in lead. The e o e, nega i e pi-
ons a e asymp o ically mo e abundan ly p oduced han
posi i e pions.
Fo comple eness, we men ion ha he e sion o he
INCL model ha was used o he p esen wo k is INCL++
5.2.9.2.
3 Thin a ge : pion-p oduc ion c oss sec ions
As discussed in Sec. 1, Gean 4 simula ions pe o med wi h
an INCL++-based physics lis yield he bes o e all e-
p oduc ion o he measu ed neu on p oduc ion o he
n_TOF spalla ion a ge , con a y o he physics lis s us-
ing he Bina y Cascade (BIC) [28] o Be ini models [29],
which o e es ima e he expe imen ally e alua ed neu on
p oduc ion by as much as 70% [10]. In Re . 10 i was hin ed
ha a possible explana ion o his di e ence could be e-
la ed o pion p oduc ion. In pa icula , i was poin ed ou
ha bo h neu al and cha ged pions could play an im-
po an ole in de e mining he p oduc ion o neu ons as
well as o he so-called p omp γ- ay componen , i.e. hose
p oduced in he i s nanoseconds o he spalla ion eac-
ions (wi h he delayed γ- ay componen p oduced la e
on om neu on cap u e eac ion and de-exci a ion o ex-
ci ed esidues). In he ollowing, he ole o seconda y pi-
ons in spalla ion a ge s is in es iga ed, s a ing om a
compa ison o heo e ical di e en ial c oss sec ions wi h
he a ailable expe imen al da a. We ema k ha he p e-
dic i e capabili y o he INCL model o he p oduc ion o
o he pa icles (in pa icula neu ons, p o ons and ligh
cha ged pa icles) below 3GeV has al eady been es ab-
lished in an ex ensi e benchma k o spalla ion models, o -
ganized unde he auspices o he IAEA [5–7].
In o de o assess he alidi y o he INCL++ and
o he models, i is e y use ul o compa e wi h one o
he mos comple e and comp ehensi e da a se on pion
p oduc ion a high ene gy. Such da a we e collec ed by
he HARP expe imen a CERN [30, 31], whe e ex en-
si e measu emen s o double-di e en ial c oss sec ions o
cha ged-pion p oduc ion in p o on- and pion-induced e-
ac ions we e pe o med. Inciden momen a o 3,5,8and
12 GeV/c we e conside ed.
3.1 In eg al pion p oduc ion
Figu es 3–5 show inclusi e pion-p oduc ion c oss sec ions
in eg a ed o e he accep ance o he HARP expe imen .
In addi ion o he INCL++ calcula ion, we show he e-
sul s o h ee o he models: Be ini [29] and Bina y Cas-
cade (BIC) [28] a e popula in anuclea -cascade models
a ailable in Gean 4, while INCL4.6 ep esen s he Liège
In anuclea Cascade model wi hou mul ipion ex ension
[32]. The di e ence be ween INCL4.6 and INCL++ clea ly
highligh s he impo ance o he ex ension, which is al-
eady sizable a he lowes inciden momen um o he
HARP da a-se (3GeV/c). The INCL4.6 model is e-
po ed o illus a e ce ain su p ising ea u es o he had onic
showe in Sec. 4, namely he ela i e insensi i eness o he
de ails o he ea men o he indi idual elemen a y in-
e ac ions.
The INCL++ and Be ini models p o ide compa ably
accu a e p edic ions. Be ini is gene ally close o he ex-
pe imen al da a o ligh a ge s, while INCL++ pe o ms
be e on hea y a ge s, such as lead, which is mos in e -
es ing o he p esen wo k and in gene al o spalla ion
neu on sou ces. P o on-nucleus da a a e gene ally be e
ep oduced han pion-nucleus da a, wi h all calcula ions
anyway being wi hin a ac o o 2 om he expe imen-
al da a, wi h he BIC model ha ing g ea e di icul ies in
ep oducing he expe imen al c oss sec ions.
Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s 5
101102
a ge mass numbe
10−3
10−2
10−1
100
101
102
103
c oss sec ion (mb)
3 GeV/c
5 GeV/c
(×10−1)
8 GeV/c
(×10−2)
12 GeV/c
(×10−3)
π+
INCL++
INCL4.6
Be ini
BIC
101102
a ge mass numbe
3 GeV/c
5 GeV/c
(×10−1)
8 GeV/c
(×10−2)
12 GeV/c
(×10−3)
π−
Figu e 3. C oss sec ions o he p oduc ion o π+(le ) and
π−( igh ) om p o on-nucleus eac ions, in eg a ed o e he
HARP angle-momen um accep ance, o di e en inciden p o-
on momen a, as unc ions o he a ge mass numbe . The lines
ep esen calcula ions by di e en models (see ex o de ails).
The expe imen al da a a e aken om Re . 30.
101102
a ge mass numbe
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
101
102
103
c oss sec ion (mb)
3 GeV/c
5 GeV/c
(×10−2)
8 GeV/c
(×10−4)
12 GeV/c
(×10−6)
π+
INCL++
INCL4.6
Be ini
BIC
101102
a ge mass numbe
3 GeV/c
5 GeV/c
(×10−2)
8 GeV/c
(×10−4)
12 GeV/c
(×10−6)
π−
Figu e 4. Same as Fig. 3, bu o π+-nucleus eac ions.
101102
a ge mass numbe
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
101
102
103
c oss sec ion (mb)
3 GeV/c
5 GeV/c
(×10−2)
8 GeV/c
(×10−4)
12 GeV/c
(×10−6)
π+
INCL++
INCL4.6
Be ini
BIC
101102
a ge mass numbe
3 GeV/c
5 GeV/c
(×10−2)
8 GeV/c
(×10−4)
12 GeV/c
(×10−6)
π−
Figu e 5. Same as Fig. 3, bu o π−-nucleus eac ions.
I is impo an o ema k ha e y ew inclusi e ex-
pe imen al da a exis o he p oduc ion o neu al pions
in p o on-nucleus and pion-nucleus eac ions. This is o
cou se mainly due o he sho li e ime o he neu al pion,
which complica es i s de ec ion. I is he e o e cus oma y
o benchma k eac ion models only on cha ged-pion p o-
duc ion. We will ollow he same app oach in he p esen
wo k. The alidi y o he in e pola ion o neu al pions
can o en be di ec ly ela ed o he goodness o he isospin-
symme y app oxima ion, which is commonly used o he
compu a ion o elemen a y c oss sec ions in in anuclea
cascade.
3.2 Double-di e en ial pion-p oduc ion c oss sec ions
Figu es 6 and 7 show double-di e en ial (momen um-angle)
c oss sec ions o inclusi e pion p oduc ion in p o on- and
pion-induced eac ions. Fo benchma king we selec wo
inciden momen a - 3and 12 GeV/c - and we ocus on he
lead a ge , which is he mos impo an o he s udy o
he n_TOF spalla ion sou ce. Fo simplici y, we limi ou
discussion o π+p oduc ion in p o on- and π−-induced
eac ions; hese esul s exhibi all he ypical ea u es o
he gene al case.
Fo he pu pose o his wo k, he mos in e es ing quan-
i y o compa e is he pion emission spec um. The c oss
sec ions o Figs. 3–5 a e de e mined by in eg a ion o he
double-di e en ial c oss sec ions in Figs. 6 and 7 o e he
momen um and angle accep ance o he HARP da a-se . I
clea ly appea s ha no model accu a ely ep oduces he
emission spec a o all angles and momen a. INCL++

6 Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s
10−2
10−1
dσ/dΩdp [mb/(s MeV/c)]
(a)
INCL++
Be ini
Bina y
(b) (c) (d)
0 200 400 600
p[MeV/c]
10−2
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(e)
0 200 400 600
p[MeV/c]
( )
0 200 400 600
p[MeV/c]
(g)
0 200 400 600
p[MeV/c]
(h)
Figu e 6. Double-di e en ial c oss sec ions o he p oduc ion o π+a 25◦(a, e), 48◦(b, ), 71◦(c, g) and 105◦(d, h),
om 3 GeV/c (a–d) and 12 GeV/c (e–h) p+Pb. The lines ep esen calcula ions by di e en models (see ex o de ails). The
expe imen al da a a e aken om Re . 30.
and Be ini a e gene ally mo e accu a e a o wa d and
backwa d angles, espec i ely, while BIC is, as al eady
no ed, a he a om he expe imen al da a. The good-
ness o he model p edic ions o his obse able is qual-
i a i ely consis en wi h he esul s o neu on p oduc-
ion in Gean 4 simula ions o he n_TOF spalla ion a -
ge , p o iding u he e idence o he undamen al ole o
pion-induced eac ions in hick spalla ion a ge s.
An in e es ing obse a ion ha can be made abou
Figs. 6 and 7 is ha INCL++ and Be ini consis en ly
show a dip in he spec a a o wa d angles (e en up o
oughly 90◦) and a ound 250 MeV/c, which is no seen in
he expe imen al da a. This de ec was also no iced by he
au ho s o Re . 29, who en a i ely a ibu ed i o insu i-
cien mode a ion by he nuclea medium. In ou opinion,
howe e , he dip is ela ed o he o ma ion and decay o
he ∆(1232) esonance, which mani es s i sel as a s ong
peak in he pion-nucleon c oss sec ion. This in ui ion is
igge ed by he obse a ion ha he posi ion o he dip
coincides app oxima ely wi h he posi ion o he esonance
in he π+N→∆c oss sec ion. Indeed, we ha e e i ied
ha he dip is insensi i e o easonable modi ica ions o
he ecombina ion (∆+N→N+N) c oss sec ion.
The mechanism leading o he o ma ion o he dip
in he model is a he simple, i one makes a ew eason-
able assump ions. Fi s , we assume ha pion p oduc ion
in INC p oceeds in wo s ages. In he i s s age, ea ly el-
emen a y collisions gene a e a s uc u eless (no dip) pion
spec um (i is easonable o assume ha pions a e p o-
duced ea ly in he eac ion because he ene gy a ailable o
pion p oduc ion quickly deg ades a e a ew collisions). In
he second s age, he gene a ed pions a e se he nucleus,
possibly unde going sca e ing and abso p ion, and pos-
sibly eme ging as ee pa icles. In his pic u e, he ea ly
pions a e a enua ed by he nuclea medium, wi h he ex-
ci a ion o he ∆(1232) esonance playing a ole in he dis-
o ion o he p is ine pion spec um, due o selec i e pion
abso p ion a he co esponding esonance ene gy. Since
Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s 7
10−2
10−1
dσ/dΩdp [mb/(s MeV/c)]
(a)
INCL++
Be ini
Bina y
(b) (c) (d)
0 200 400 600
p[MeV/c]
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(e)
0 200 400 600
p[MeV/c]
( )
0 200 400 600
p[MeV/c]
(g)
0 200 400 600
p[MeV/c]
(h)
Figu e 7. Same as Fig. 6, bu o 3 GeV/c (a–d) and 12 GeV/c (e–h) π−+Pb eac ions.
he dip is insensi i e o he ecombina ion c oss sec ion
and o he esonance li e ime, and since ∆ esonances (in
INCL) can only be abso bed by ecombina ion, we con-
clude ha he in e media e ∆ esonances mos ly decay
back o pion-nucleon pai s. In p inciple, he momen um
o he pion should all back in he dip egion. Howe e ,
while he o ma ion and decay o he in e media e ∆ es-
onances does no modi y he pion momen um dis ibu ion,
i does ac on he angula dis ibu ion. I one makes he
easonable assump ion ha he p is ine pion spec um is
sensibly o wa d-peaked, hen he decay o he in e medi-
a e ∆ esonances will edis ibu e pions om he o wa d
angles o all angles. This mani es s i sel as a dip a o -
wa d angles in he double-di e en ial spec a.
While his explana ion migh hold alid o he dip ob-
se ed in he model calcula ions, i is no clea whe he i
also applies o he da a. A hin o a dip may be seen in he
e y o wa d angles, bu in gene al da a seems o indica e
ha in eali y he dip, i any, is less p onounced han wha
p edic ed by he models. We pe o med some es s and we
e i ied ha he dip disappea s i he π+N→∆c oss
sec ion is a i icially educed by abou a ac o o 2. One
can also ac on he wid h o he ∆ esonance peak in he
π+N→∆en ance channel: in e es ingly, ei he inc eas-
ing o dec easing he wid h o he B ei -Wigne -like peak
will supp ess he dip in he calcula ions. Theo e ical cal-
cula ions [e.g. 33] indica e ha in-medium ∆ esonances
should be b oade han he co esponding ee pa icles,
al hough unambiguous quan i a i e indica ions a e s ill
missing [34]. INCL al eady gene a es pa o his medium
e ec (on he esonance li e ime) h ough he applica ion
o Pauli blocking on he esonance decay and h ough ∆
abso p ion. Fo consis ency one should also modi y he
c oss sec ion o he o ma ion p ocess o e lec his. I e-
mains o be seen i a ealis ic modi ica ion o he ∆wid h
(in he spi i o e.g. Re s. 35, 36) can econcile he calcu-
la ions wi h he expe imen al da a.
Fo he sake o comple eness, we men ion ha he e
is disag eemen abou he scien i ic adequa eness o he
HARP da a analysis. A g oup o o me HARP collabo-
a o s ( he HARP-CDP g oup) ha e published a e isi ed
analysis o he aw HARP da a, which has spa ked a long
8 Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(a) (b) (c) (d) INCL++
Be ini
Bina y
0 400 800
p[MeV/c]
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(e)
0 400 800
p[MeV/c]
( )
0 400 800
p[MeV/c]
(g)
0 400 800
p[MeV/c]
(h)
Figu e 8. Double-di e en ial c oss sec ions o he p oduc ion
o π+a 0◦–25.8◦(a, e), 25.8◦–41.0◦(b, ), 41.0◦–50.6◦(c, g)
and 50.6◦–59.0◦(d, h), om 12.3 GeV/c (a–d) and 17.5 GeV/c
(e–h) p+Au. The lines ep esen calcula ions by di e en mod-
els (see ex o de ails). The expe imen al da a a e aken om
Re . 39.
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(a) (b) (c) (d) INCL++
Be ini
Bina y
0 400 800
p[MeV/c]
10−1
100
dσ/dΩdp [mb/(s MeV/c)]
(e)
0 400 800
p[MeV/c]
( )
0 400 800
p[MeV/c]
(g)
0 400 800
p[MeV/c]
(h)
Figu e 9. Same as Fig. 8, bu o he p oduc ion o π−.
and well-documen ed con o e sy [37]. Re . 38 con ains
di ec compa isons o he double-di e en ial momen um-
angle c oss sec ions, bu only o he smalles angle (25◦)
and o 3and 8GeV/c beam momen a (Figs. 12 and 13
in hei pape ). On his limi ed basis, i is di icul o de-
cide whe he he HARP-CDP c oss sec ions a e compa i-
ble wi h he dip in he calcula ions, al hough he ac ha
he HARP-CDP da a seem o be consis en ly smalle han
he HARP da a a low momen um is encou aging.
Gi en his s a e o a ai s, i is su ely wise and ins uc-
i e o conside o he da a-se s. Figu es 8 and 9 show e-
sul s o he calcula ion o double-di e en ial pion-emission
c oss sec ions o 12.3and 17.5GeV/c p o ons on gold
a ge s, compa ed o he da a om Re . 39. The ene gy
and he a ge o he 12.3GeV/c da a-se a e close o
100101102103104
ene gy [MeV]
10−5
10−4
10−3
10−2
10−1
100
101
dN eac/dE[MeV−1sou ce−1]
neu ons
p o ons
pions
INCL++
INCL4.6
Figu e 10. Inciden -ene gy dis ibu ion o nuclea eac ions
induced wi hin he had onic cascade by p o ons, neu ons
and pions, no malized o one p ima y p o on, as calcula ed
by he INCL model wi h (INCL++, solid lines) and wi h-
ou (INCL4.6, dashed lines) mul ipion ex ension, wi hin he
Gean 4 simula ion o he n_TOF spalla ion a ge (beam mo-
men um o 20 GeV/c).
he HARP da a, Figs. 6 and 7. Howe e , when compa ing
he wo da a-se s, i is impo an o keep in mind ha 1)
he momen um accep ance is la ge in Chemakin’s da a,
and 2) he measu ed angles a e smalle : he la ges mea-
su emen angle in Chemakin’s da a-se alls be ween he
second and he hi d HARP measu emen angle. I one
makes abs ac ion o hese di e ences, he models appea
o beha e consis en ly o e all he Figs. 6–9. The e o e,
we do no see any clea indica ion ha he HARP da a
should be ejec ed.
In iew o hese di icul ies, new, high-accep ance da a
ocusing on he pion p oduc ion in high-ene gy p o on-
induced eac ion would be highly desi able. Toge he wi h
cha ged pions, di ec measu emen s o π0p oduc ion would
p o ide undamen al in o ma ion ha could con ibu e
conside ably o he op imiza ion o he INC models.
4 Thick a ge : pions in he n_TOF
spalla ion a ge
While hin- a ge double-di e en ial c oss sec ion can p o-
ide some indica ions on he abili y o he models o co -
ec ly p edic pion p oduc ion, he s uc u e o he had onic
showe s ha ake place in he spalla ion a ge , and in
pa icula he ole played by seconda y pions in he p o-
duc ion o neu ons and pho ons, can only be s udied by
means o dedica ed MC simula ions o he spalla ion p o-
cess and compa ison wi h a ailable expe imen al da a. In
his espec , we ha e chosen in his wo k o pe o m u -
he simula ions o he n_TOF spalla ion a ge wi h he
Gean 4 oolki . Be o e analysing he esul s o he simu-
la ions, i is con enien o b ie ly desc ibe he oolki and
Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s 9
he implemen a ion o he MC simula ions o he n_TOF
case.
4.1 The Gean 4 oolki
Gean 4 (GEome y ANd T anspo ) is a oolki o he
simula ion o pa icle anspo and de ec o esponse [12,
13]. The Gean amily o codes was o iginally de eloped o
he needs o he high-ene gy-physics communi y. Howe e ,
since he beginning he a ay o physics models has been
cons an ly expanding o encompass applica ions a lowe
ene gy. In pa icula , Gean 4 has been success ully used,
since se e al yea s, o desc ibe he anspo o neu ons
down o he mal ene gy, using poin -wise c oss-sec ion
om e alua ed lib a ies [40]. These de elopmen s ecen ly
igge ed new wo k on he use o Gean 4 o he simula-
ion o spalla ion neu on sou ces. Recen ly, Gean 4 sim-
ula ions pe o med o he n_TOF sou ce we e bench-
ma ked agains expe imen al esul s [10], such as he neu-
on luence and esolu ion unc ion, and yielded in e es -
ing esul s which will be sho ly desc ibed in he ollowing
subsec ion.
Physics models in Gean 4 a e o ganized and collec ed
in “physics lis s”, which a e speci ica ions o he phys-
ical p ocesses (and he associa ed models) ha should
be used in he simula ion. The names o he a ailable
Gean 4 physics lis s a e o en ob ained by conca ena ing
he names o he models used in he had onic sec o , in
dec easing o de o inciden ene gy. Thus, o ins ance,
he FTFP_INCLXX_HP physics lis , a ound which much
o he p esen wo k e ol es, elies on he F i io + p e-
equilib ium model (FTFP) a high ene gy, he INCL++
model a in e media e ene gies, and he Neu onHP model
a low ene gy.
This wo k is based on Gean 4 10.1; howe e , he INCL++
model wi hin Gean 4 was manually upg aded o 5.2.9.4,
which is he e sion ha has been dis ibu ed wi h Gean 4
10.2 (Decembe 2015).
4.2 The n_TOF simula ion
The n_TOF spalla ion a ge is a wa e -cooled lead cylin-
de su ounded by an aluminum con aine and by a neu-
on mode a o . I s s uc u e is desc ibed in de ail in Re s. 8,
10, 11. A 20 GeV/c p o on beam impinges on he base o
he lead cylinde a an angle o app oxima ely 10◦. The
lead a ge cylinde can be conside ed as hick, in he sense
ha i s size ( adius 30 cm, leng h 40 cm) is la ge compa ed
o he p o on mean ee pa h o inelas ic collisions a he
beam ene gy (∼15 cm). The e o e, he p ima y p o on
o en igge s a nuclea eac ion inside he Pb a ge and
ini ia es a had onic showe which e en ually leads o he
p oduc ion o a la ge numbe o pa icles. A no e abou
ou nomencla u e: we e e o all “non-p ima y” pa icles
as seconda ies, ega dless o he eac ion gene a ion hey
appea in, in opposi ion o he “p ima y” pa icle inciden
on he spalla ion a ge .
Among he pa icles escaping om he spalla ion a -
ge , we a e pa icula ly in e es ed in neu ons, which a e
mode a ed in wa e , ha can be ei he no mal o bo a ed,
and collima ed owa ds he expe imen al a eas. Simula-
ions o he n_TOF spalla ion a ge ha e ocused on he
ep oduc ion o he measu ed ene gy dependence, eso-
lu ion unc ion, and spa ial dis ibu ion o he neu ons
en e ing he i s expe imen al a ea (EAR1) [8, 10]. The
expec ed lux in he di ec ion o he second, new expe -
imen al a ea (EAR2) was also s udied in a ecen pa-
pe [11]. As shown in Re s. 10, 11, hese measu ed quan-
i ies a e bes ep oduced by he simula ions using he
FTFP_INCLXX_HP and QGSP_INCLXX_HP physics
lis s. Fo p o on-nucleus eac ions, hese physics lis s use
he Liège In anuclea Cascade model (INCL++) om
1MeV o 20 GeV inciden ene gy, and ei he he F i io
+ p e-equilib ium model (FTFP) o he Qua k-Gluon-
S ing + p e-equilib ium model om 15 GeV upwa ds. In
he egion whe e he wo model o e lap (15–20 GeV), he
choice o he model is andomly sampled, wi h linea ly-
in e pola ed p obabili ies be ween he in e al endpoin s
(a s anda d p ocedu e in Gean 4). Since he p ima y p o-
on beam ene gy is ∼19 GeV (20 GeV/c), i is clea ha
he FTFP o QGSP will ypically be used a mos o
he simula ion o he i s inelas ic p o on-nucleus eac-
ion3; he es o he had onic showe is domina ed by
he INCL++ model. Fo his eason, we limi ou analysis
on he FTFP_INCLXX_HP physics lis . The ollowing
sec ion in oduces a global desc ip ion o INCL++, wi h
pa icula ocus on i s pion dynamics.
4.3 Analysis o seconda y eac ions
We s a by illus a ing how nuclea eac ions in he a -
ge a e dis ibu ed wi h espec o he ype o he inciden
pa icle and i s ene gy. Figu e 10 shows he dis ibu ion
o he p ojec ile ene gy o nuclea eac ions induced by
p o ons, neu ons and pions. Each dis ibu ion is no mal-
ized o he o al numbe o eac ions pe p ima y p o-
on induced by he indica ed pa icle. No e ha Fig. 10
includes he eac ions induced by he p ima y p o ons,
which appea as a small peak close o he beam ene gy,
whose in eg al oughly amoun s o 0.91 eac ions pe in-
ciden p o on; his is consis en wi h he hickness o he
spalla ion a ge , which is o he o de o 2.5nuclea mean
ee pa hs a he beam ene gy. No e also ha his plo
does no include elas ic collisions. This choice mainly ol-
lows om he conside a ion ha elas ic sca e ing on lead
nuclei does no sensibly modi y he p ojec ile ene gy o
nucleons and pions; in addi ion, a high ene gy, he elas ic
angula dis ibu ion is sensibly o wa d-peaked and is un-
likely o a ec he global low o ene gy and momen um
wi hin he spalla ion a ge .
Table 1 p esen s he in eg al eac ion a es o e se-
lec ed anges o inciden ene gy, as calcula ed by Gean 4
simula ions using he INCL model wi h (INCL++) and
3Excep o cou se o e en s o speci ic classes, in ol ing
small ene gy losses, like e.g. quasi-elas ic sca e ing.
16 Da ide Mancusi e al.: On he ole o seconda y pions in spalla ion a ge s
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