and

$$\label{nmas1}
\lim_{\gamma\rightarrow 0} n^+(p_3) = 2 \pi N \delta(p_3).$$

Using Eq.(\[nmas1\]) we have the following expression for the particle density $N$ in the vicinity of $p_3=0$

$$\label{densityTcero}
N \simeq \frac{1}{2 \pi} \lim_{\gamma\rightarrow 0}\int_{-\infty}^{\infty} 2 \pi N \frac{\gamma}{p_{3}^2 + \gamma^2} dp_3 = N \int_{-\infty}^{\infty} \delta(p_3)dp_3.$$

The delta behaviour of the Bose-Einstein distribution $ n^+(p_3)$ for low temperatures or high fields is depicted in Fig. 3. Left panel of Fig. 3 shows the boson distribution as a function of $p_3$ for a fixed value of temperature $T=10^7 K$ and several values of the magnetic field. The maximum of the curves increases and move to the left when the magnetic field grows. Right panel of Fig. 3 shows the boson distribution as a function of $p_3$ for a fixed value of the magnetic field $B=0.1 B_c$ and different values of the temperatures. The maximum of the curves increases and shift to the left with the decrease of the temperature. Fig. 3 illustrates that although there is not a critical temperature (or field), as the limits $T \rightarrow 0$ or $B \rightarrow B_c$ are approached, the bosons concentrate in the ground state and its neighboring states. Therefore, the system has a diffuse BEC.

