Isothermal vertical reactor for a chemical reaction, comprising: - a shell with a longitudinal axis (A-A); - at least a gas inlet for a fresh gas charge and a product outlet; - at least a first gas-permeable wall parallel to said axis, and a second gas-permeable wall parallel to said longitudinal axis (A-A), so that a distribution chamber is defined between the first gas-permeable wall and the shell of the reactor, and a product collecting chamber in communication with said product outlet is defined between the second gas-permeable wall and the shell; - a catalytic bed accommodated inside the shell, the gas permeable walls of said distribution chamber and collecting chamber facing said catalytic bed; - a heat exchanger embedded in said catalytic bed, the reactor being characterized in that: - the heat exchanger comprises a bundle of U tubes, each of said U tubes having two straight portions (13a, 13c) fixed to a bottom tube sheet or manifold and connected by a U-shaped portion, thus forming a U-shaped end portion of the tube bundle, wherein a first straight portion of said U tubes fixed to said bottom tube sheet or manifold is in communication with a fluid distribution chamber while a second straight portion of said U tubes fixed to said bottom tube sheet or manifold is in communication with a fluid collecting chamber, fluid distribution chamber and fluid collecting chamber being delimited by a partition wall; - said gas inlet is disposed to direct the fresh charge in an upper chamber of the reactor, over the catalytic bed; - the catalytic bed and the distribution chamber are in communication with said upper chamber of the reactor, so that during operation of the reactor, a first portion of the fresh charge can enter directly the catalytic bed, passing through the U-shaped portion of the tube bundle, and a second portion of the fresh charge can enter the inlet gas-distribution chamber, the first portion flowing in the catalytic bed and towards the product collecting chamber with a mixed axial-transversal flow, the second portion flowing in the catalytic bed, from the gas distribution chamber towards said collecting chamber, with a substantially transversal flow. - a shell with a longitudinal axis (A-A); - at least a gas inlet for a fresh gas charge and a product outlet; - at least a first gas-permeable wall parallel to said axis, and a second gas-permeable wall parallel to said longitudinal axis (A-A), so that a distribution chamber is defined between the first gas-permeable wall and the shell of the reactor, and a product collecting chamber in communication with said product outlet is defined between the second gas-permeable wall and the shell; - a catalytic bed accommodated inside the shell, the gas permeable walls of said distribution chamber and collecting chamber facing said catalytic bed; - a heat exchanger embedded in said catalytic bed, - the heat exchanger comprises a bundle of U tubes, each of said U tubes having two straight portions (13a, 13c) fixed to a bottom tube sheet or manifold and connected by a U-shaped portion, thus forming a U-shaped end portion of the tube bundle, wherein a first straight portion of said U tubes fixed to said bottom tube sheet or manifold is in communication with a fluid distribution chamber while a second straight portion of said U tubes fixed to said bottom tube sheet or manifold is in communication with a fluid collecting chamber, fluid distribution chamber and fluid collecting chamber being delimited by a partition wall; - said gas inlet is disposed to direct the fresh charge in an upper chamber of the reactor, over the catalytic bed; - the catalytic bed and the distribution chamber are in communication with said upper chamber of the reactor, so that during operation of the reactor, a first portion of the fresh charge can enter directly the catalytic bed, passing through the U-shaped portion of the tube bundle, and a second portion of the fresh charge can enter the inlet gas-distribution chamber, the first portion flowing in the catalytic bed and towards the product collecting chamber with a mixed axial-transversal flow, the second portion flowing in the catalytic bed, from the gas distribution chamber towards said collecting chamber, with a substantially transversal flow.