Subthreshold particle production

To produce a pion (mass ~ 140 MeV for charged pions, 135 MeV for neutral pions) in a NN collision, a lab energy of at least ~ 290 (~ 280) MeV is required.

However, it has been known for a long time that in nucleus-nucleus collisions, pions may be created at energies significantly below 280 MeV/nucleon.

First evidence for such pion production in AA collisions was obtained as early as 1948 with 300-380 MeV alpha particles.

More recently (1982), CERN experiments with 12C at 60 MeV/nucleon showed evidence of positive and negative pion production.

Since 1982, several groups have studied pion production between 25 and 100 MeV/nucleon.

How to explain such “subthreshold” pion production?

First explanations of such effects were given in terms of coupling the bound nucleon Fermi momenta to the momentum of relative motion between the two nuclei.

Such mechanism is not expected to work for very low beam energies. On the basis of single nucleon-nucleon collision model (with realistic momentum distributions), threshold energies around 50 MeV/nucleon can be predicted.

At lower energies and very close to the absolute threshold, one must invoke the presence of collective effects.

In the low energy limit, close to the absolute threshold, the process of pion creation requires the transformation of most (or all) the projectile’s kinetic energy into a single degree of freedom (creation of a new particle).

In contrast to processes where light particles and low energy photons are emitted in a nucleus-nucleus collision (where the statistical description of the collision plays a major role) here the coherent aspects of the collision should be evidenced.

The absolute threshold for pion production in (symmetric) heavy ion collisions vs mass number of the two nuclei.

Pion production close to the absolute threshold requires that many nucleons in the projectile and the target act cooperatively to convert their energy into the pion mass

Lab Coulomb energy

How many nucleons must cooperate to produce a pion of a given kinetic energy?

Miminum number of target nucleons required in a 14N-induced reaction to produce pions of different kinetic energies

0 MeV

250 MeV

* = Exp. Data

Experimental methods for charged pions

Since the mechanism is close to the absolute threshold, low energy pions are expected.

For charged pions, basically two methods have been employed:

Magnetic spectrometers

Range telescopes

Magnetic spectrometers

Note that the charged pion lifetime is 26 ns.

Example: 93% of 100 MeV pions decay after 30 m flight path

A typical set-up includes a magnetic field (fixed or variable) and a focal plane detector, made by scintillators and/or drift chambers.

Advantages: good resolution

Disadvantages: small solid angles

Pion flight paths may vary from 1-2 m to 30 m.

CLAMSUD spectrometer (Catania), used in Moscow (1991-1995) and Uppsala (1995-2000)

CLAMSUD spectrometer@Uppsala

Range telescopes

A multi-element scintillator telescope may be used to discriminate pions against protons

At 100 MeV/nucleons, usually there are 10000 proton for each pion

Advantage: Simple devices, large solid angles

Disadvantages: Poor energy resolution, some contamination

Next generation (exclusive) experiments employed multidetectors

Example: GANIL Mur+Tonneau

NP A519(1990)213

Neutral pion detection

Neutral pions decay (B.R. 98.8%) into two gammas, with 0.87 x 10-

16 s lifetime

Detection of neutral pions require the coincidence detection of two gammas in a large background of low energy gammas (about 107-108 per neutral pion) from nuclear deexcitation. For a pion at rest, the two gammas have 70 MeV each.

π0

γ1

γ2

First set-up’s for neutral pion detection used small arrays of Pb-glass scintillators

Sizes and granularity of scintillators determine the capability to reconstruct the electromagnetic shower initiated by the high-energy photon

Energy resolution and angular resolution of the two gammas determine the overall resolution on the neutral pionFrom J.Stachel et al,

PRC33(1986)1420

Next generation experiments used large solid angle arrays, able to detect not only photons from the pion decay, but also coincident particles

(exclusive experiments)

One example is the MEDEA BaF2 crystal ball, which was used for the first time in GANIL at the end of 80’s, before being installed in Catania

A 180 BaF2 array (from 30º to 140º, complemented by 120 phoswich detectors able to cover from 10º to 30º

MEDEA

Another multidetector widely used for photons and neutral mesons is TAPS, installed in several Laboratories (GANIL, GSI, Mainz, Groningen,..)

Each BaF2 module has exagonal shape, with a charged particle veto in front of it.

Various configurations for

TAPS

TAPS configuration at KVI

TAPS configuration at GSI, GANIL

When the energy resolution is not so good, it is better to extract the energy of pions from

where the asymmetry parameter is given by

With this choice the invariant mass is given by

and the kinetic energy and pion emission angle by

Pion reconstruction

For simulation results using MEDEA as a neutral pion detector, see NIM A306(1991)283

Main results from inclusive experiments on subthreshold pion production

As early as 1987, several inclusive experiments on subthreshold pion (charged and neutral) production in heavy ion collisions were available

MS: Magnetic Spectrometer

RT: Range Telescope

LG: Lead Glass scintillators

Pion kinetic energy distributions

All spectra exhibit a broad maximum at low pion kinetic energies (~10 MeV) and a nearly exponential decay

dσ/dT = const exp(-T/E0)

For the case reported here, the inverse slope parameter E0 is about 23 MeV

N+Ni @35 MeV/A

Angular distributions

Energy integrated angular distributions are usually forward/backward symmetric.

However, angular distributions are different for low energy and high energy pions, with a backward rise for the highest energies.

Forward peaked distributions are expected for pion emission from a source moving in the beam direction, with a forward/backward symmetry in the source rest frame.

Backward peaking difficult to explain:

Role of reabsorption and source location?

N+Ni @35 MeV/A

Integrated pion cross sections

The integrated cross sections increase with increasing target size

Solid line: (AT )2/3

Expected for pion production from single nucleon-nucleon collisions

At higher bombarding energies, data are in agreement with single nucleon-nucleon collisions. At lower energies, discrepancies observed.

Possible interpretations:

- Pion production implies a source extended more than just 2 nucleons

- Pion reabsorption effects for large targets play a major role

Invariant cross sections

To investigate the pion production mechanism another relevant information is the invariant cross section, especially if large enough angular and energy ranges are explored.

If the invariant cross section is plotted as a function of rapidity and transverse momentum, all the information of the pion-emitting source is contained in one variable (y), while the other variable (pt) is free from kinematical effects and is determined only by internal characteristics of the system emitting the pions.

Invariant cross sections/2

Contour plots of iso-invariant cross sections may be obtained if enough statistics is available

For a single moving source emitting pions, the contour plot should be symmetric about the source rapidity

N + Ni @35 MeV/A

For symmetric projectile-target systems, the source rapidity has been found to be one half of the projectile rapidity. For any system, a source rapidity intermediate between yb/2 and y(c.m.) is found.

Here, average rapidity is very close to 0 (target), smaller than yb/2.

For low bombarding energies, there are evidences that the projectile will stop in the c.m. system before traversing the target nucleus. This will lead to shadowing effects in the forward direction, and then to a downward shift in rapidity (even to negative values!)

All data and conclusions are strongly affected by pion reabsorption effects!

Reabsorption effects

Experimental data on pion absorption are usually available at

high pion energies

ground state nuclear matter

Here, we are dealing with

low energy pions

which are reabsorbed in

excited nuclear matter

Optical model calculations which reproduce pion absorbption data predict a maximum pion mean free path λabs around 3.6 fm for 25 MeV pions, with smaller values at lower and higher pion energies ( 3 fm at 10 MeV, 1.7 fm at 100 MeV).

Consider that the combined system N+Ni has a radius of 7 fm at 50% density

Pion reabsorption effects even in a light system cannot be neglected, and modify in a drastic way the primary energy/angular distributions

Example of a Monte Carlo simulation of the pion reabsorption for different source location

z

Z=0

Z axis along the beam, with z=0 at the center of the combined projectile-target system

Z=0

Z=-4 fm

Z=+4 fm

Activity:

Simulate the geometrical overlap of two nuclei (for simplicity assume them as discs in a 2D-plane), assume isotropic angular distribution and thermal energy distribution of emitted pions, introduce a mean free path of pions (dependent on pion kinetic energy?) and some distribution for the location of the source.

Evaluate the modifications of angular and energy distributions due to pion reabsorption

Systematics of cross section vs bombarding energy

To compare cross sections measured for different target and projectile combinations, they are normalized to (Ap AT)2/3

For subthreshold energies, cross sections are strongly dependent on bombarding energy.

(a factor 100000 between 20 and 90 MeV/A)

So, what can be learned from inclusive experiments on subthreshold pion production?

Different models have tried to explain the known data:

Single nucleon-nucleon collision model

Cooperative models

Collective/coherent models

The original idea that due to the Fermi motion of the nucleons inside the nuclei, in a single NN collision there could be enough relative energy to produce a pion, seems to work only at energies slightly below the threshold (100-150 MeV/A).

This approach fails at low bombarding energies (20-100 MeV/A).

At 84 MeV/A the predicted cross sections are already a factor 1000 lower than observed. Reabsorption effects still reduce the predicted cross sections.

At 20-84 MeV/A the disagreement is even worse

Single nucleon-nucleon collision models

Single nucleon-nucleon collision models/2

Moreover:

Inverse slope parameters predicted by such models are much smaller (a factor 2) than measured

Source velocity in single NN collision models should be yb/2. Observed values are close to 0.

For integrated cross sections, a (AT)2/3 dependence is predicted, whereas many data do not agree with this behaviour.

Cooperative models

Single nucleon-nucleon collision models fail at very low bombarding energies.

One alternative is a model involving the cooperative action of several target and projectile nucleons.

Within this model, two approaches gave been used: one is based on multiple off-shell collisions (Shiam and Knoll, NP A426(1984)606), the other on a thermal description (Aichelin and Bertsch, Phys.Lett.138B(1984)350).

Both give comparable (and good) results at energies 50-100 MeV/A, but underpredict data at lower (25-50 MeV/A) energies.

Collective or coherent models

How much energy is left to the system, after the pion is created?

Pion kinetic energy spectra, reported as a function of the energy available in the c.m. after pion emission. The zero on this scale marks the kinematical limit, where the pion carries out ALL the available energy.

In some cases, we are very close to the kinematical limit!

Near the kinematical limit, all spectra seem to merge together, and the differential cross section scales with total available energy in the c.m., rather than the energy per nucleon (or small number of nucleons).

In other words, the relevant quantity seems the total c.m. energy, not the energy per nucleon. The process may be called pionic fusion.

In such case, a fully coherent description is needed.

Some evidence of pionic fusion has been observed especially for light systems (3He+A, A<10). No data exist for heavy systems.

More recently (1991) some investigation has been done around 100 MeV/A with 12C+12C, to search for coherent pion production.

The following process was considered

where the projectile is excited to 15.1 MeV, decaying by photon emission. During the (peripheral) collision, the target is excited, with pion emission.

The experiment was carried out by searching for coincidences between 12C, 15.1 MeV photons, and one high-energy photon originating from neutral pion decay (neutral pions not identified).

Energy spectrum of photons in coincidence with 12C

9 events found!

Another collective approach is the pionic bremmstrahlung. In this model, the projectile is coherently slowed down with pion emission.

No clear evidence of such process exist, even though some experiments have searched for it.

Example: peripheral pion production in projectile break-up at 95 MeV/A, Phys.Lett. B316(1993)240.

The role of exclusive vs inclusive experiments on pion production at subthreshold energies

Large arrays of detectors able to detect neutral pions may be used for fully exclusive experiments (not simply coincidence experiments between pions and something else).

Two examples: MEDEA, TAPS

Inclusive and exclusive experiments on subthreshold pion production were carried out in GANIL with 95 MeV/nucleon Ar beams.

Neutral pions were measured in coincidence with charged particles.

Invariant mass spectrum of neutral pions, Ar+Al @95 MeV/A

Some results

Detailed inclusive differential cross sections of neutral pions were obtained for the first time in small angular bins, compared to microscopic BNV calculations

Ar+Al @95 MeV/A

w/o reabsorption

Where are pions created in heavy ion collisions at subthreshold energies?

It is reasonable to assume that most of them are created in central collisions, but only after the first exclusive experiments, this could be experimentally demonstrated.

Several global variables were used to determine the impact parameter in a quantitative way

The charged multiplicity for pion events is strongly different from inclusive events!

(Note the log scale)

Ar + Al, 95 MeV/A

Angular distributions are very different for low energy and high energy pions:

Indication of different mechanisms and reabsorption effects

Exclusive experiments on pion production at subthreshold energies allowed to investigate different aspects of the problem

The importance of statistical processes through the correlation between pions and light fragments

The role of nuclear stopping in pion production

The reabsorption effect in nuclear matter (pion shadowing)

The formation and decay of the Δ-resonance, through the correlation between pion and protons

Subthreshold production of other particles

In addition to pions, other particles may be created below the NN energy threshold by some of the above mechanisms

Examples:

Kaon and η production around 100 MeV/A

Kaon production in AA collision around 100 MeV/A

The process N+N -> K+ Λ N requires an energy of 670 MeV, which means 1.58 GeV in the lab system for pA

K+ production is then a very unlikely process at 100 MeV/A!

Some data exist for the Ar+C, Ti, Ta @92 MeV/A

(Legrain et al., Phys.Rev. C59(1999)1464

Some experimental detail

Mean lifetime of K+ = 12.4 ns

Main decay channel:

K+ -> μ+ ν (64 %)

Kaons are stopped

Muons from kaon decay are detected in a range telescope

Some events found and cross section extracted

Cross section Systematics

In the analysis of such data on meson production, it is usual to extract from the measured cross section the probability per participant nucleon

from the ratio of experimental cross section to the geometrical cross section and average number of participants.

The geometrical cross section is

The average number of participant nucleons is evaluated by

Meson production probability

Search for η production around 100 MeV/A

A search for possible detection of η-mesons at 95 MeV/A was made (NIM A338(1997)109 with the MEDEA BaF2 array

To search events from η-meson decay at 100 MeV/A is a real challenge!

Detailed simulations of the possible contributions to the invariant mass spectra were done by GEANT

Experimental data from Ar+Al, Ni, Sn, Au

2 candidate events

Cross section systematics

Results for η decay

Activity:

Investigate the kinematics of the pion (or eta) decay

Evaluate the minimum and maximum energy of the two gammas from neutral pion and from η decay as a function of their kinetic energy.

Activity:

Reconstruct neutral pion from GEANT simulated electromagnetic showers in a BaF2 array