Production of deuterium, tritium, and ${}^3\mathbf{He}$ in central Pb + Pb collisions at $20A,30A,40A,80A$, and $158A$ GeV at the CERN Super Proton Synchrotron

Production of $d,t$, and ${}^3\mathrm{He}$ nuclei in central $\mathrm{Pb}+\mathrm{Pb}$ interactions was studied at five collision energies ($\sqrt{s_{NN}}=6.3$, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN Super Proton Synchrotron. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and ${}^3\mathrm{He}$ were determined as a function of transverse mass at all energies.

Figure 1

(a) Energy loss $dE/dx$ versus mass squared from $\mathrm{Pb}+\mathrm{Pb}$ at $20A$ GeV for the momentum interval $6<p<8 \mathrm{GeV}/c$. Deuteron and triton candidates are selected within the $3\sigma$ particle identification (PID) ellipses indicated by the dashed lines. (b) Mass-squared distribution after a $dE/dx$ upper limit cut (see text). The solid line indicates the best fit with two Gaussians (the dotted lines) and the background (the dash-dotted line).

Figure 2

(a) Energy loss $dE/dx$ measured in the MTPC as a function of rigidity for charged tracks from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $40A$ GeV. The dashed curves indicate the PID cut boundaries used for selection of ${}^3\mathrm{He}$. (b) Distribution of $dE/dx$ in the momentum interval $8<p<10 \mathrm{GeV}/c$. A fit of a Gaussian signal plus background is shown by the solid curve. Black vertical lines indicate the selection window for ${}^3\mathrm{He}$.

Figure 3

The NA49 phase-space coverage in terms of $y$ and $m_t$ at $20A$ GeV for deuterons (a), tritons (b), ${}^3\mathrm{He}$ (c) and at $158A$ GeV for deuterons (d), tritons (e), ${}^3\mathrm{He}$ (f).

Figure 4

Invariant $p_t$ spectra of ${}^3\mathrm{He}$ at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). Only statistical errors are shown. The distributions near midrapidity are drawn to scale; other spectra are scaled down by successive powers of 5 for clarity. The same scaling factor is used for two rapidity slices that are symmetric about midrapidity $\left(y=0\right)$.

Figure 5

Invariant $p_t$ spectra of $d$ at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). Only statistical errors are shown.

Figure 6

Invariant $p_t$ spectra of $t$ at $20A\text{–}158A\text{GeV}$. Only statistical errors are shown.

Figure 7

$p_t$ spectra of ${}^3\mathrm{He}$ in rapidity bins of $\left|\mathrm{\Delta }y\right|=0.3$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A$ GeV. Fits with a sum of two exponentials are plotted by the dashed curves; fits with a single exponential are plotted by dotted curves (see text for more detail).

Figure 8

Rapidity distributions for ${}^3\mathrm{He}$ at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). The solid symbols show the measurements and the open symbols represent the data points reflected about midrapidity. The error bars correspond to the quadratic sum of statistical and systematic errors. Dashed and dot-dashed lines indicate the functional forms used to extrapolate to $4\pi$ yields (see text for more detail). The NA44 experimental data on $t$ are taken from Ref. [28].

Figure 9

Rapidity distributions for $d$ at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). The solid symbols show the measurements and the open symbols represent the data points reflected about midrapidity. The error bars correspond to the quadratic sum of statistical and systematic errors. Dashed and dot-dashed lines indicate the functional forms used to extrapolate to $4\pi$ yields (see text for more detail). The NA44 experimental data on $d$ are taken from Ref. [28].

Figure 10

$4\pi$ yield of ${}^3\mathrm{He}$ in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$. The NA49 data (red squares) are the average of the results for the Fit A and Fit B extrapolations (see text for detail). Thermal model calculations (see text) are shown by blue circles; the inset shows the ratio of the experimental data to the thermal model predictions. Symbols for experimental data and model predictions have been displaced for clarity in presentation.

Figure 11

$4\pi$ yield of deuterons in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$. The NA49 data (red squares) are the average of the results for the Fit A and Fit B extrapolations (see text for detail). Thermal model calculations (see text) are shown by blue circles; the inset shows the ratio of the experimental data to the thermal model predictions. Symbols for experimental data and model predictions have been displaced for clarity in presentation.

Figure 12

Rapidity distributions for ${}^3\mathrm{He}$ (a) and deuterons (b) from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$ versus normalized rapidity $y/y_{\text{beam}}$. The solid symbols show the measurements and the open symbols represent the data points reflected around midrapidity. The error bars correspond to the quadratic sum of statistical and systematic errors. Dashed lines indicate parabolic fits to the rapidity spectra (see text for more detail).

Figure 13

The ratio $b/a$ of the fit parameters obtained for the rapidity spectra of ${}^3\mathrm{He}$ (circles) and $d$ (squares) from central $\mathrm{Pb}+\mathrm{Pb}$ collisions as a function of $\sqrt{s_{NN}}$.

Figure 14

Values of $dN/dy$ at midrapidity (see text) as a function of mass number $A (p,d,{}^3\mathrm{He})$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$. The dashed lines represent the fit to an exponential dependence [see text Eq. (5)]. Values of $dN/dy$ for $d$ were divided by the spin factor 3/2 (see text for more detail).

Figure 15

Penalty factor from the cluster yields at mid-rapidity (solid symbols) and $4\pi$ multiplicities (open circles) in central $A+A$ collisions. Red circles represent the NA49 data, the AGS measurement (blue triangle) is from [24], and the green star indicates the result from the ALICE experiment [42]. The thermal statistical model estimates are from [8, 36, 37, 38] (see text for detail).

Figure 16

(a) Invariant midrapidity $p_t$ spectra of $p,d$, and ${}^3\mathrm{He}$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $30A$ GeV. (b) Invariant yield of clusters at several values of $p_t/A$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $30A$ GeV(values for $d$ were divided by the spin factor 3/2). (c) Penalty factor $P$ from the cluster yields at several values of $p_t/A$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$. (d) Excitation function for the penalty factor at $p_t/A$ near zero and $p_t/A=0.8 \mathrm{GeV}/c$. AGS data are from [24]; the result from the STAR Collaboration was reported in Ref. [43].

Figure 17

$m_t$ spectra of ${}^3\mathrm{He}$ in rapidity slices from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (d). The spectra are scaled down by a factor of 3 successively. Only statistical errors are plotted. Dashed curves indicate the fits to the spectra with a sum of two exponential functions.

Figure 18

Mean transverse mass for ${}^3\mathrm{He}$ as a function of $y/y_{\text{beam}}$ from central $\mathrm{Pb}+\mathrm{Pb}$ at $20A\text{–}158A\text{GeV}$. Results for the forward and backward hemispheres were averaged (see text). Dashed lines indicate fits to a Gaussian.

Figure 19

(a) $\langle m_t\rangle -m$ at midrapidity vs $\sqrt{s_{NN}}$ for $A=3$ clusters from central $A+A$ collisions at energies available at SPS, AGS, and RHIC. (b) The width ${\sigma }_{y/y_{\text{beam}}}$ of the Gaussian fitted to the rapidity dependence of $\langle m_t\rangle -m$ (see Fig. 18) for ${}^3\mathrm{He}$ versus $\sqrt{s_{NN}}$.

Figure 20

Invariant $m_t$ spectra from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$ for tritons (a) and deuterons (b).

Figure 21

Mass dependence of $\langle m_t\rangle -m$ in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A\text{–}158A\text{GeV}$. Linear fits to the data points are indicated by dashed lines.

Figure 22

Energy dependence of the source temperature $T$ (a) and average collective transverse velocity $\langle \beta \rangle$ (b) at the kinetic freeze-out in central $A+A$ collisions. The NA49 data from the $m_t$ versus mass analysis (see text for detail) are indicated by green circles; those from blast-wave (BW) fits of $m_t$ spectra of hadrons from NA49 are depicted by blue squares; red stars are the STAR-BES results from a BW analysis of hadron spectra reported in Ref. [50].

Figure 23

Blast-wave (BW) motivated fits to midrapidity $m_t$ spectra of $\pi ,K,p$, and $\overline{p}$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $40A$ GeV. Data from Refs. [35, 39, 51].

Figure 24

Ratio of $t$ to ${}^3\mathrm{He}$ yields as a function of $p_t$ from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). The dashed lines show the results of fits to a constant.

Figure 25

$n/p,t/{}^3\mathrm{He}$, and ${\pi }^{-}/{\pi }^{+}$ ratios in central $A+A$ collisions.

Figure 26

Coalescence parameter $B_2$ as a function of $m_t-m$ for deuterons from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). The dashed lines represent fits with an exponential in $m_t$.

Figure 27

Coalescence parameter $B_3$ as a function of $m_t-m$ for ${}^3\mathrm{He}$ nuclei from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A$ (a), $30A$ (b), $40A$ (c), $80A$ (d), and $158A$ GeV (e). The dashed lines represent fits with an exponential in $m_t$.

Figure 28

Coalescence parameters $B_2$ and $B_3$ from central $A+A$ collisions.

Figure 29

Coalescence radii $R_{\text{coal}}$ for $A=2$ (squares) and $A=3$ (circles) nuclei from central $A+A$ collisions.